A universal numerical approach for nonlinear mathematic programming problems is presented with an application of ratios of first-order differentials/differences of objective functions to constraint functions with resp...A universal numerical approach for nonlinear mathematic programming problems is presented with an application of ratios of first-order differentials/differences of objective functions to constraint functions with respect to design variables. This approach can be efficiently used to solve continuous and, in particular, discrete programmings with arbitrary design variables and constraints. As a search method, this approach requires only computations of the functions and their partial derivatives or differences with respect to design variables, rather than any solution of mathematic equations. The present approach has been applied on many numerical examples as well as on some classical operational problems such as one-dimensional and two-dimensional knap-sack problems, one-dimensional and two-dimensional resource-distribution problems, problems of working reliability of composite systems and loading problems of machine, and more efficient and reliable solutions are obtained than traditional methods. The present approach can be used without limitation of modeling scales of the problem. Optimum solutions can be guaranteed as long as the objective function, constraint functions and their First-order derivatives/differences exist in the feasible domain or feasible set. There are no failures of convergence and instability when this approach is adopted.展开更多
In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method （CHIIP） for convex nonlinear programming problems. For any convex n...In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method （CHIIP） for convex nonlinear programming problems. For any convex nonlinear programming, without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method.展开更多
An improved genetic algorithm（IGA） based on a novel selection strategy to handle nonlinear programming problems is proposed.Each individual in selection process is represented as a three-dimensional feature vector w...An improved genetic algorithm（IGA） based on a novel selection strategy to handle nonlinear programming problems is proposed.Each individual in selection process is represented as a three-dimensional feature vector which is composed of objective function value,the degree of constraints violations and the number of constraints violations.It is easy to distinguish excellent individuals from general individuals by using an individuals＇ feature vector.Additionally,a local search（LS） process is incorporated into selection operation so as to find feasible solutions located in the neighboring areas of some infeasible solutions.The combination of IGA and LS should offer the advantage of both the quality of solutions and diversity of solutions.Experimental results over a set of benchmark problems demonstrate that IGA has better performance than other algorithms.展开更多
A penalized interior point approach for constrained nonlinear programming is examined in this work. To overcome the difficulty of initialization for the interior point method, a problem equivalent to the primal proble...A penalized interior point approach for constrained nonlinear programming is examined in this work. To overcome the difficulty of initialization for the interior point method, a problem equivalent to the primal problem via incorporating an auxiliary variable is constructed. A combined approach of logarithm barrier and quadratic penalty function is proposed to solve the problem. Based on Newton＇s method, the global convergence of interior point and line search algorithm is proven. Only a finite number of iterations is required to reach an approximate optimal solution. Numerical tests are given to show the effectiveness of the method.展开更多
By redefining the multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, say, u2_i, i=1, 2, ..., m, nonnegative constraints imposed on inequality constra...By redefining the multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, say, u2_i, i=1, 2, ..., m, nonnegative constraints imposed on inequality constraints in Karush-Kuhn-Tucker necessary conditions are removed. For constructing the Lagrange neural network and Lagrange multiplier method, it is no longer necessary to convert inequality constraints into equality constraints by slack variables in order to reuse those results dedicated to equality constraints, and they can be similarly proved with minor modification. Utilizing this technique, a new type of Lagrange neural network and a new type of Lagrange multiplier method are devised, which both handle inequality constraints directly. Also, their stability and convergence are analyzed rigorously.展开更多
In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local ...In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local maximum, we utilize a merit function to guide the iterates toward a local minimum. Especially, we add the parameter ε to the Newton system when calculating the decrease directions. The global convergence is achieved by the decrease of a merit function. Furthermore, the numerical results confirm that the algorithm can solve this kind of problems in an efficient way.展开更多
One of the most important issues in numerical calculations is finding simple roots of nonlinear equations. This topic is one of the oldest challenges in science and engineering. Many important problems in engineering,...One of the most important issues in numerical calculations is finding simple roots of nonlinear equations. This topic is one of the oldest challenges in science and engineering. Many important problems in engineering, to achieve the result need to solve a nonlinear equation. Thus, the formulation of a recursive relationship with high order of convergence and low time complexity is very important. This paper provides a modification to the Weerakoon-Fernando and Parhi-Gupta methods. It is shown that, in each iterate, the improved method requires three evaluations of the function and two evaluations of the first derivatives of function. The proposed with the Kou et al., Neta, Parhi-Gupta, Thukral and Mir et al. methods have been applied to a collection of 12 test problem. The results show that proposed approach significantly reduces the number of function calls when compared to the above methods. The numerical examples show that the proposed method is more efficiency than other methods in this class, such as sixth-order method of Parhi-Gupta or eighth-order method of Mir et al. and Thukral. We show that the order of convergence the proposed method is 9 and also, the modified method has the efficiency of .展开更多
In this article, a finite volume element algorithm is presented and discussed for the numerical solutions of a time-fractional nonlinear fourth-order diffusion equation with time delay. By choosing the second-order sp...In this article, a finite volume element algorithm is presented and discussed for the numerical solutions of a time-fractional nonlinear fourth-order diffusion equation with time delay. By choosing the second-order spatial derivative of the original unknown as an additional variable, the fourth-order problem is transformed into a second-order system. Then the fully discrete finite volume element scheme is formulated by using L1approximation for temporal Caputo derivative and finite volume element method in spatial direction. The unique solvability and stable result of the proposed scheme are proved. A priori estimate of L2-norm with optimal order of convergence O(h2+τ2−α)where τand hare time step length and space mesh parameter, respectively, is obtained. The efficiency of the scheme is supported by some numerical experiments.展开更多
Evolutionary algorithms have been extensively utilized in practical applications.However,manually designed population updating formulas are inherently prone to the subjective influence of the designer.Genetic programm...Evolutionary algorithms have been extensively utilized in practical applications.However,manually designed population updating formulas are inherently prone to the subjective influence of the designer.Genetic programming(GP),characterized by its tree-based solution structure,is a widely adopted technique for optimizing the structure of mathematical models tailored to real-world problems.This paper introduces a GP-based framework(GPEAs)for the autonomous generation of update formulas,aiming to reduce human intervention.Partial modifications to tree-based GP have been instigated,encompassing adjustments to its initialization process and fundamental update operations such as crossover and mutation within the algorithm.By designing suitable function sets and terminal sets tailored to the selected evolutionary algorithm,and ultimately derive an improved update formula.The Cat Swarm Optimization Algorithm(CSO)is chosen as a case study,and the GP-EAs is employed to regenerate the speed update formulas of the CSO.To validate the feasibility of the GP-EAs,the comprehensive performance of the enhanced algorithm(GP-CSO)was evaluated on the CEC2017 benchmark suite.Furthermore,GP-CSO is applied to deduce suitable embedding factors,thereby improving the robustness of the digital watermarking process.The experimental results indicate that the update formulas generated through training with GP-EAs possess excellent performance scalability and practical application proficiency.展开更多
This paper addresses the tracking control problem of a class of multiple-input–multiple-output nonlinear systems subject to actuator faults.Achieving a balance between input saturation and performance constraints,rat...This paper addresses the tracking control problem of a class of multiple-input–multiple-output nonlinear systems subject to actuator faults.Achieving a balance between input saturation and performance constraints,rather than conducting isolated analyses,especially in the presence of frequently encountered unknown actuator faults,becomes an interesting yet challenging problem.First,to enhance the tracking performance,Tunnel Prescribed Performance(TPP)is proposed to provide narrow tunnel-shape constraints instead of the common over-relaxed trumpet-shape performance constraints.A pair of non-negative signals produced by an auxiliary system is then integrated into TPP,resulting in Saturation-tolerant Prescribed Performance(SPP)with flexible performance boundaries that account for input saturation situations.Namely,SPP can appropriately relax TPP when needed and decrease the conservatism of control design.With the help of SPP,our developed Saturation-tolerant Prescribed Control(SPC)guarantees finite-time convergence while satisfying both input saturation and performance constraints,even under serious actuator faults.Simulations are conducted to illustrate the effectiveness of the proposed SPC.展开更多
Under investigation is the n-component nonlinear Schrödinger equation with higher-order effects,which describes the ultrashort pulses in the birefringent fiber.Based on the Lax pair,the eigenfunction and generali...Under investigation is the n-component nonlinear Schrödinger equation with higher-order effects,which describes the ultrashort pulses in the birefringent fiber.Based on the Lax pair,the eigenfunction and generalized Darboux transformation are derived.Next,we construct several novel higher-order localized waves and classified them into three categories:(i)higher-order rogue waves interacting with bright/antidark breathers,(ii)higher-order breather fission/fusion,(iii)higherorder breather interacting with soliton.Moreover,we explore the effects of parameters on the structure,collision process and energy distribution of localized waves and these characteristics are significantly different from previous ones.Finally,the dynamical properties of these solutions are discussed in detail.展开更多
Planning for water quality management is important for facilitating sustainable socio-economic development;however, the planning is also complicated by a variety of uncertainties and nonlinearities. In this study, an ...Planning for water quality management is important for facilitating sustainable socio-economic development;however, the planning is also complicated by a variety of uncertainties and nonlinearities. In this study, an interval-parameter fuzzy robust nonlinear programming (IFRNP) model was developed for water quality management to deal with such difficulties. The developed model incorporated interval nonlinear programming (INP) and fuzzy robust programming (FRP) methods within a general optimization framework. The developed IFRNP model not only could explicitly deal with uncertainties represented as discrete interval numbers and fuzzy membership functions, but also was able to deal with nonlinearities in the objective function.展开更多
An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstr...An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstrained minimizers of the augmented Lagrangian function on the space of problem variables and the local minimizers of the original constrained problem. Furthermore, under some assumptions, the relationship was also established between the global solutions of the augmented Lagrangian function on some compact subset of the space of problem variables and the global solutions of the constrained problem. Therefore, f^om the theoretical point of view, a solution of the inequality constrained problem and the corresponding values of the Lagrange multipliers can be found by the well-known method of multipliers which resort to the unconstrained minimization of the augmented Lagrangian function presented.展开更多
In this paper a new approach for obtaining an approximation global optimum solution of zero-one nonlinear programming (0-1 NP) problem which we call it Parametric Linearization Approach (P.L.A) is proposed. By using t...In this paper a new approach for obtaining an approximation global optimum solution of zero-one nonlinear programming (0-1 NP) problem which we call it Parametric Linearization Approach (P.L.A) is proposed. By using this approach the problem is transformed to a sequence of linear programming problems. The approximately solution of the original 0-1 NP problem is obtained based on the optimum values of the objective functions of this sequence of linear programming problems defined by (P.L.A).展开更多
We propose an exact penalty approach for solving mixed integer nonlinear programming (MINLP) problems by converting a general MINLP problem to a finite sequence of nonlinear programming (NLP) problems with only contin...We propose an exact penalty approach for solving mixed integer nonlinear programming (MINLP) problems by converting a general MINLP problem to a finite sequence of nonlinear programming (NLP) problems with only continuous variables. We express conditions of exactness for MINLP problems and show how the exact penalty approach can be extended to constrained problems.展开更多
In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with ...In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.展开更多
This study proposes a novel approach to optimizing individual work schedules for book digitization using mixed-integer programming (MIP). By leveraging the power of MIP solvers, we aimed to minimize the overall digiti...This study proposes a novel approach to optimizing individual work schedules for book digitization using mixed-integer programming (MIP). By leveraging the power of MIP solvers, we aimed to minimize the overall digitization time while considering various constraints and process dependencies. The book digitization process involves three key steps: cutting, scanning, and binding. Each step has specific requirements and limitations such as the number of pages that can be processed simultaneously and potential bottlenecks. To address these complexities, we formulate the problem as a one-machine job shop scheduling problem with additional constraints to capture the unique characteristics of book digitization. We conducted a series of experiments to evaluate the performance of our proposed approach. By comparing the optimized schedules with the baseline approach, we demonstrated significant reductions in the overall processing time. In addition, we analyzed the impact of different weighting schemes on the optimization results, highlighting the importance of identifying and prioritizing critical processes. Our findings suggest that MIP-based optimization can be a valuable tool for improving the efficiency of individual work schedules, even in seemingly simple tasks, such as book digitization. By carefully considering specific constraints and objectives, we can save time and leverage resources by carefully considering specific constraints and objectives.展开更多
Nonlinear science is a fundamental area of physics research that investigates complex dynamical systems which are often characterized by high sensitivity and nonlinear behaviors.Numerical simulations play a pivotal ro...Nonlinear science is a fundamental area of physics research that investigates complex dynamical systems which are often characterized by high sensitivity and nonlinear behaviors.Numerical simulations play a pivotal role in nonlinear science,serving as a critical tool for revealing the underlying principles governing these systems.In addition,they play a crucial role in accelerating progress across various fields,such as climate modeling,weather forecasting,and fluid dynamics.However,their high computational cost limits their application in high-precision or long-duration simulations.In this study,we propose a novel data-driven approach for simulating complex physical systems,particularly turbulent phenomena.Specifically,we develop an efficient surrogate model based on the wavelet neural operator(WNO).Experimental results demonstrate that the enhanced WNO model can accurately simulate small-scale turbulent flows while using lower computational costs.In simulations of complex physical fields,the improved WNO model outperforms established deep learning models,such as U-Net,Res Net,and the Fourier neural operator(FNO),in terms of accuracy.Notably,the improved WNO model exhibits exceptional generalization capabilities,maintaining stable performance across a wide range of initial conditions and high-resolution scenarios without retraining.This study highlights the significant potential of the enhanced WNO model for simulating complex physical systems,providing strong evidence to support the development of more efficient,scalable,and high-precision simulation techniques.展开更多
The nonlinear post-buckling response of functionally graded(FG)copper matrix plates enforced by graphene origami auxetic metamaterials(GOAMs)is investigated in the currentwork.The auxeticmaterial properties of the pla...The nonlinear post-buckling response of functionally graded(FG)copper matrix plates enforced by graphene origami auxetic metamaterials(GOAMs)is investigated in the currentwork.The auxeticmaterial properties of the plate are controlled by graphene content and the degree of origami folding,which are graded across the thickness of the plate.Thematerial properties of the GOAM plate are evaluated using genetic micro-mechanicalmodels.Governing nonlinear eigenvalue problems for the post-buckling response of the GOAM composite plate are derived using the virtual work principle and a four-variable nonlinear shear deformation theory.A novel differential quadrature method(DQM)algorithm is developed to solve the nonlinear eigenvalue problem.Detailed parametric studies are presented to explore the effects of graphene content,folding degree,and GO distribution patterns on the post-buckling responses of GOAM plates.Results show that high tunability in post-buckling characteristics can be achieved by using GOAM.FunctionallyGradedGraphene OrigamiAuxeticMetamaterials(FG-GOAM)plates can be used in aerospace structures to improve their structural performance and response.展开更多
Due to scale effects,micromechanical resonators offer an excellent platform for investigating the intrinsic mechanisms of nonlinear dynamical phenomena and their potential applications.This review focuses on mode-coup...Due to scale effects,micromechanical resonators offer an excellent platform for investigating the intrinsic mechanisms of nonlinear dynamical phenomena and their potential applications.This review focuses on mode-coupled micromechanical resonators,highlighting the latest advancements in four key areas:internal resonance,synchronization,frequency combs,and mode localization.The origin,development,and potential applications of each of these dynamic phenomena within mode-coupled micromechanical systems are investigated,with the goal of inspiring new ideas and directions for researchers in this field.展开更多
文摘A universal numerical approach for nonlinear mathematic programming problems is presented with an application of ratios of first-order differentials/differences of objective functions to constraint functions with respect to design variables. This approach can be efficiently used to solve continuous and, in particular, discrete programmings with arbitrary design variables and constraints. As a search method, this approach requires only computations of the functions and their partial derivatives or differences with respect to design variables, rather than any solution of mathematic equations. The present approach has been applied on many numerical examples as well as on some classical operational problems such as one-dimensional and two-dimensional knap-sack problems, one-dimensional and two-dimensional resource-distribution problems, problems of working reliability of composite systems and loading problems of machine, and more efficient and reliable solutions are obtained than traditional methods. The present approach can be used without limitation of modeling scales of the problem. Optimum solutions can be guaranteed as long as the objective function, constraint functions and their First-order derivatives/differences exist in the feasible domain or feasible set. There are no failures of convergence and instability when this approach is adopted.
文摘In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method （CHIIP） for convex nonlinear programming problems. For any convex nonlinear programming, without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method.
基金supported by the National Natural Science Foundation of China (60632050)National Basic Research Program of Jiangsu Province University (08KJB520003)
文摘An improved genetic algorithm（IGA） based on a novel selection strategy to handle nonlinear programming problems is proposed.Each individual in selection process is represented as a three-dimensional feature vector which is composed of objective function value,the degree of constraints violations and the number of constraints violations.It is easy to distinguish excellent individuals from general individuals by using an individuals＇ feature vector.Additionally,a local search（LS） process is incorporated into selection operation so as to find feasible solutions located in the neighboring areas of some infeasible solutions.The combination of IGA and LS should offer the advantage of both the quality of solutions and diversity of solutions.Experimental results over a set of benchmark problems demonstrate that IGA has better performance than other algorithms.
基金supported by the National Natural Science Foundation of China (Grant No.10771133)the Shanghai Leading Academic Discipline Project (Grant Nos.J50101, S30104)
文摘A penalized interior point approach for constrained nonlinear programming is examined in this work. To overcome the difficulty of initialization for the interior point method, a problem equivalent to the primal problem via incorporating an auxiliary variable is constructed. A combined approach of logarithm barrier and quadratic penalty function is proposed to solve the problem. Based on Newton＇s method, the global convergence of interior point and line search algorithm is proven. Only a finite number of iterations is required to reach an approximate optimal solution. Numerical tests are given to show the effectiveness of the method.
文摘By redefining the multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, say, u2_i, i=1, 2, ..., m, nonnegative constraints imposed on inequality constraints in Karush-Kuhn-Tucker necessary conditions are removed. For constructing the Lagrange neural network and Lagrange multiplier method, it is no longer necessary to convert inequality constraints into equality constraints by slack variables in order to reuse those results dedicated to equality constraints, and they can be similarly proved with minor modification. Utilizing this technique, a new type of Lagrange neural network and a new type of Lagrange multiplier method are devised, which both handle inequality constraints directly. Also, their stability and convergence are analyzed rigorously.
文摘In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local maximum, we utilize a merit function to guide the iterates toward a local minimum. Especially, we add the parameter ε to the Newton system when calculating the decrease directions. The global convergence is achieved by the decrease of a merit function. Furthermore, the numerical results confirm that the algorithm can solve this kind of problems in an efficient way.
文摘One of the most important issues in numerical calculations is finding simple roots of nonlinear equations. This topic is one of the oldest challenges in science and engineering. Many important problems in engineering, to achieve the result need to solve a nonlinear equation. Thus, the formulation of a recursive relationship with high order of convergence and low time complexity is very important. This paper provides a modification to the Weerakoon-Fernando and Parhi-Gupta methods. It is shown that, in each iterate, the improved method requires three evaluations of the function and two evaluations of the first derivatives of function. The proposed with the Kou et al., Neta, Parhi-Gupta, Thukral and Mir et al. methods have been applied to a collection of 12 test problem. The results show that proposed approach significantly reduces the number of function calls when compared to the above methods. The numerical examples show that the proposed method is more efficiency than other methods in this class, such as sixth-order method of Parhi-Gupta or eighth-order method of Mir et al. and Thukral. We show that the order of convergence the proposed method is 9 and also, the modified method has the efficiency of .
文摘In this article, a finite volume element algorithm is presented and discussed for the numerical solutions of a time-fractional nonlinear fourth-order diffusion equation with time delay. By choosing the second-order spatial derivative of the original unknown as an additional variable, the fourth-order problem is transformed into a second-order system. Then the fully discrete finite volume element scheme is formulated by using L1approximation for temporal Caputo derivative and finite volume element method in spatial direction. The unique solvability and stable result of the proposed scheme are proved. A priori estimate of L2-norm with optimal order of convergence O(h2+τ2−α)where τand hare time step length and space mesh parameter, respectively, is obtained. The efficiency of the scheme is supported by some numerical experiments.
文摘Evolutionary algorithms have been extensively utilized in practical applications.However,manually designed population updating formulas are inherently prone to the subjective influence of the designer.Genetic programming(GP),characterized by its tree-based solution structure,is a widely adopted technique for optimizing the structure of mathematical models tailored to real-world problems.This paper introduces a GP-based framework(GPEAs)for the autonomous generation of update formulas,aiming to reduce human intervention.Partial modifications to tree-based GP have been instigated,encompassing adjustments to its initialization process and fundamental update operations such as crossover and mutation within the algorithm.By designing suitable function sets and terminal sets tailored to the selected evolutionary algorithm,and ultimately derive an improved update formula.The Cat Swarm Optimization Algorithm(CSO)is chosen as a case study,and the GP-EAs is employed to regenerate the speed update formulas of the CSO.To validate the feasibility of the GP-EAs,the comprehensive performance of the enhanced algorithm(GP-CSO)was evaluated on the CEC2017 benchmark suite.Furthermore,GP-CSO is applied to deduce suitable embedding factors,thereby improving the robustness of the digital watermarking process.The experimental results indicate that the update formulas generated through training with GP-EAs possess excellent performance scalability and practical application proficiency.
基金supported by the National Research Foundation Singapore under its AI Singapore Programme(Award Number:[AISG2-GC-2023-007]).
文摘This paper addresses the tracking control problem of a class of multiple-input–multiple-output nonlinear systems subject to actuator faults.Achieving a balance between input saturation and performance constraints,rather than conducting isolated analyses,especially in the presence of frequently encountered unknown actuator faults,becomes an interesting yet challenging problem.First,to enhance the tracking performance,Tunnel Prescribed Performance(TPP)is proposed to provide narrow tunnel-shape constraints instead of the common over-relaxed trumpet-shape performance constraints.A pair of non-negative signals produced by an auxiliary system is then integrated into TPP,resulting in Saturation-tolerant Prescribed Performance(SPP)with flexible performance boundaries that account for input saturation situations.Namely,SPP can appropriately relax TPP when needed and decrease the conservatism of control design.With the help of SPP,our developed Saturation-tolerant Prescribed Control(SPC)guarantees finite-time convergence while satisfying both input saturation and performance constraints,even under serious actuator faults.Simulations are conducted to illustrate the effectiveness of the proposed SPC.
基金Project supported by the National Natural Science Foundation of China(Grant No.12271096)the Natural Science Foundation of Fujian Province(Grant No.2021J01302)。
文摘Under investigation is the n-component nonlinear Schrödinger equation with higher-order effects,which describes the ultrashort pulses in the birefringent fiber.Based on the Lax pair,the eigenfunction and generalized Darboux transformation are derived.Next,we construct several novel higher-order localized waves and classified them into three categories:(i)higher-order rogue waves interacting with bright/antidark breathers,(ii)higher-order breather fission/fusion,(iii)higherorder breather interacting with soliton.Moreover,we explore the effects of parameters on the structure,collision process and energy distribution of localized waves and these characteristics are significantly different from previous ones.Finally,the dynamical properties of these solutions are discussed in detail.
文摘Planning for water quality management is important for facilitating sustainable socio-economic development;however, the planning is also complicated by a variety of uncertainties and nonlinearities. In this study, an interval-parameter fuzzy robust nonlinear programming (IFRNP) model was developed for water quality management to deal with such difficulties. The developed model incorporated interval nonlinear programming (INP) and fuzzy robust programming (FRP) methods within a general optimization framework. The developed IFRNP model not only could explicitly deal with uncertainties represented as discrete interval numbers and fuzzy membership functions, but also was able to deal with nonlinearities in the objective function.
文摘An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstrained minimizers of the augmented Lagrangian function on the space of problem variables and the local minimizers of the original constrained problem. Furthermore, under some assumptions, the relationship was also established between the global solutions of the augmented Lagrangian function on some compact subset of the space of problem variables and the global solutions of the constrained problem. Therefore, f^om the theoretical point of view, a solution of the inequality constrained problem and the corresponding values of the Lagrange multipliers can be found by the well-known method of multipliers which resort to the unconstrained minimization of the augmented Lagrangian function presented.
文摘In this paper a new approach for obtaining an approximation global optimum solution of zero-one nonlinear programming (0-1 NP) problem which we call it Parametric Linearization Approach (P.L.A) is proposed. By using this approach the problem is transformed to a sequence of linear programming problems. The approximately solution of the original 0-1 NP problem is obtained based on the optimum values of the objective functions of this sequence of linear programming problems defined by (P.L.A).
文摘We propose an exact penalty approach for solving mixed integer nonlinear programming (MINLP) problems by converting a general MINLP problem to a finite sequence of nonlinear programming (NLP) problems with only continuous variables. We express conditions of exactness for MINLP problems and show how the exact penalty approach can be extended to constrained problems.
基金Supported by the National Natural Science Foundation of China(11671403,11671236,12101192)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.
文摘This study proposes a novel approach to optimizing individual work schedules for book digitization using mixed-integer programming (MIP). By leveraging the power of MIP solvers, we aimed to minimize the overall digitization time while considering various constraints and process dependencies. The book digitization process involves three key steps: cutting, scanning, and binding. Each step has specific requirements and limitations such as the number of pages that can be processed simultaneously and potential bottlenecks. To address these complexities, we formulate the problem as a one-machine job shop scheduling problem with additional constraints to capture the unique characteristics of book digitization. We conducted a series of experiments to evaluate the performance of our proposed approach. By comparing the optimized schedules with the baseline approach, we demonstrated significant reductions in the overall processing time. In addition, we analyzed the impact of different weighting schemes on the optimization results, highlighting the importance of identifying and prioritizing critical processes. Our findings suggest that MIP-based optimization can be a valuable tool for improving the efficiency of individual work schedules, even in seemingly simple tasks, such as book digitization. By carefully considering specific constraints and objectives, we can save time and leverage resources by carefully considering specific constraints and objectives.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.42005003 and 41475094)。
文摘Nonlinear science is a fundamental area of physics research that investigates complex dynamical systems which are often characterized by high sensitivity and nonlinear behaviors.Numerical simulations play a pivotal role in nonlinear science,serving as a critical tool for revealing the underlying principles governing these systems.In addition,they play a crucial role in accelerating progress across various fields,such as climate modeling,weather forecasting,and fluid dynamics.However,their high computational cost limits their application in high-precision or long-duration simulations.In this study,we propose a novel data-driven approach for simulating complex physical systems,particularly turbulent phenomena.Specifically,we develop an efficient surrogate model based on the wavelet neural operator(WNO).Experimental results demonstrate that the enhanced WNO model can accurately simulate small-scale turbulent flows while using lower computational costs.In simulations of complex physical fields,the improved WNO model outperforms established deep learning models,such as U-Net,Res Net,and the Fourier neural operator(FNO),in terms of accuracy.Notably,the improved WNO model exhibits exceptional generalization capabilities,maintaining stable performance across a wide range of initial conditions and high-resolution scenarios without retraining.This study highlights the significant potential of the enhanced WNO model for simulating complex physical systems,providing strong evidence to support the development of more efficient,scalable,and high-precision simulation techniques.
文摘The nonlinear post-buckling response of functionally graded(FG)copper matrix plates enforced by graphene origami auxetic metamaterials(GOAMs)is investigated in the currentwork.The auxeticmaterial properties of the plate are controlled by graphene content and the degree of origami folding,which are graded across the thickness of the plate.Thematerial properties of the GOAM plate are evaluated using genetic micro-mechanicalmodels.Governing nonlinear eigenvalue problems for the post-buckling response of the GOAM composite plate are derived using the virtual work principle and a four-variable nonlinear shear deformation theory.A novel differential quadrature method(DQM)algorithm is developed to solve the nonlinear eigenvalue problem.Detailed parametric studies are presented to explore the effects of graphene content,folding degree,and GO distribution patterns on the post-buckling responses of GOAM plates.Results show that high tunability in post-buckling characteristics can be achieved by using GOAM.FunctionallyGradedGraphene OrigamiAuxeticMetamaterials(FG-GOAM)plates can be used in aerospace structures to improve their structural performance and response.
基金supported by the National Key Research and Development Program of China(No.2022YFB3203600)the National Natural Science Foundation of China(Nos.12202355,12132013,and 12172323)the Zhejiang Provincial Natural Science Foundation of China(No.LZ22A020003)。
文摘Due to scale effects,micromechanical resonators offer an excellent platform for investigating the intrinsic mechanisms of nonlinear dynamical phenomena and their potential applications.This review focuses on mode-coupled micromechanical resonators,highlighting the latest advancements in four key areas:internal resonance,synchronization,frequency combs,and mode localization.The origin,development,and potential applications of each of these dynamic phenomena within mode-coupled micromechanical systems are investigated,with the goal of inspiring new ideas and directions for researchers in this field.
