In this paper, we study linear static Stac kelberg problems with multiple leaders-followers in which each decision maker wi thin his group may or may not cooperate. An exact penalty function method is dev eloped. The ...In this paper, we study linear static Stac kelberg problems with multiple leaders-followers in which each decision maker wi thin his group may or may not cooperate. An exact penalty function method is dev eloped. The duality gaps of the followers’ problems are appended to the leaders’ objective function with a penalty. The structure leads to the decomposition of the composite problem into a series of linear programmings leading to an efficie nt algorithm. We prove that local optimality is reached for an exact penalty fun ction and illustrate the method with three examples. The model in this paper ext ends the stackelberg leader-follower model.展开更多
In the criminal justice system, the criminal execution though is the last part, but with the conviction and sentencing of the system have the same importance. Criminal conviction and sentencing execution is guaranteed...In the criminal justice system, the criminal execution though is the last part, but with the conviction and sentencing of the system have the same importance. Criminal conviction and sentencing execution is guaranteed to achieve, but also fairness and justice contained in the Criminal Code. In criminal law enforcement issues related to research more deeply refined today, supervision of Criminal changes have also been made to perform individually and have a very important significance. A direct result of the implementation of the activities of Criminal debtor prison of term prison sentences and the way to change the location, and the status of implementation as well as criminal penalties for the personal interests are closely related, and therefore it is a very, important enforcement regime. Under our current legal environment, the high amount of crime, large numbers of people in custody are restdting in criminal arduous tasks. It is coupled with the existing legal provisions for change-flawed execution of supervision that is extremely prone to change in the course of execution carried favoritism, money corruption. Meanwhile, the new introduction of the ＂Criminal Law Amendment eight,＂ is for which the commutation, parole perform content changes made adjustments and changes.But for the first time, it provides for community corrections system officially to be incorporated into China＇ s Criminal Law among but the corresponding lack of prosecutorial oversight and other content specific legal provisions, changes are related to the implementation of community Corrections supervision given probation, parole, probation and other penalties to bring the practical operation of the nroblerns.展开更多
For smooth optimization problem with equMity constraints, new continuously differentiable penalty function is derived. It is proved exact in the sense that local optimizers of a nonlinear program are precisely the opt...For smooth optimization problem with equMity constraints, new continuously differentiable penalty function is derived. It is proved exact in the sense that local optimizers of a nonlinear program are precisely the optimizers of the associated penalty function under some nondegeneracy assumption. It is simple in the sense that the penalty function only includes the objective function and constrained functions, and it doesn＇t include their gradients. This is achieved by augmenting the dimension of the program by a variable that controls the weight of the penalty terms.展开更多
Regularized minimization problems with nonconvex, nonsmooth, even non-Lipschitz penalty functions have attracted much attention in recent years, owing to their wide applications in statistics, control,system identific...Regularized minimization problems with nonconvex, nonsmooth, even non-Lipschitz penalty functions have attracted much attention in recent years, owing to their wide applications in statistics, control,system identification and machine learning. In this paper, the non-Lipschitz ?_p(0 < p < 1) regularized matrix minimization problem is studied. A global necessary optimality condition for this non-Lipschitz optimization problem is firstly obtained, specifically, the global optimal solutions for the problem are fixed points of the so-called p-thresholding operator which is matrix-valued and set-valued. Then a fixed point iterative scheme for the non-Lipschitz model is proposed, and the convergence analysis is also addressed in detail. Moreover,some acceleration techniques are adopted to improve the performance of this algorithm. The effectiveness of the proposed p-thresholding fixed point continuation(p-FPC) algorithm is demonstrated by numerical experiments on randomly generated and real matrix completion problems.展开更多
For ill-posed bilevel programming problem,the optimistic solution is always the best decision for the upper level but it is not always the best choice for both levels if the authors consider the model's satisfacto...For ill-posed bilevel programming problem,the optimistic solution is always the best decision for the upper level but it is not always the best choice for both levels if the authors consider the model's satisfactory degree in application.To acquire a more satisfying solution than the optimistic one to realize the two levels' most profits,this paper considers both levels' satisfactory degree and constructs a minimization problem of the two objective functions by weighted summation.Then,using the duality gap of the lower level as the penalty function,the authors transfer these two levels problem to a single one and propose a corresponding algorithm.Finally,the authors give an example to show a more satisfying solution than the optimistic solution can be achieved by this algorithm.展开更多
The guide-weight method is introduced to solve the topology optimization problems of thermoelastic structures in this paper.First,the solid isotropic microstructure with penalization(SIMP)with different penalty factor...The guide-weight method is introduced to solve the topology optimization problems of thermoelastic structures in this paper.First,the solid isotropic microstructure with penalization(SIMP)with different penalty factors is selected as a material interpolation model for the thermal and mechanical fields.The general criteria of the guide-weight method is then presented.Two types of iteration formulas of the guide-weight method are applied to the topology optimization of thermoelastic structures,one of which is to minimize the mean compliance of the structure with material constraint,whereas the other one is to minimize the total weight with displacement constraint.For each type of problem,sensitivity analysis is conducted based on SIMP model.Finally,four classical 2-dimensional numerical examples and a 3-dimensional numerical example considering the thermal field are selected to perform calculation.The factors that affect the optimal topology are discussed,and the performance of the guide-weight method is tested.The results show that the guide-weight method has the advantages of simple iterative formula,fast convergence and relatively clear topology result.展开更多
In this paper, we give a solving approach based on a logarithmic-exponential multiplier penalty function for the constrained minimization problem. It is proved exact in the sense that the global optimizers of a nonlin...In this paper, we give a solving approach based on a logarithmic-exponential multiplier penalty function for the constrained minimization problem. It is proved exact in the sense that the global optimizers of a nonlinear problem are precisely the global optimizers of the logarithmic-exponential multiplier penalty problem.展开更多
For the semi-infinite programming （SIP） problem, the authors first convert it into an equivalent nonlinear programming problem with only one inequality constraint by using an integral function, and then propose a sm...For the semi-infinite programming （SIP） problem, the authors first convert it into an equivalent nonlinear programming problem with only one inequality constraint by using an integral function, and then propose a smooth penalty method based on a class of smooth functions. The main feature of this method is that the global solution of the penalty function is not necessarily solved at each iteration, and under mild assumptions, the method is always feasible and efficient when the evaluation of the integral function is not very expensive. The global convergence property is obtained in the absence of any constraint qualifications, that is, any accumulation point of the sequence generated by the algorithm is the solution of the SIP. Moreover, the authors show a perturbation theorem of the method and obtain several interesting results. Furthermore, the authors show that all iterative points remain feasible after a finite number of iterations under the Mangasarian-Fromovitz constraint qualification. Finally, numerical results are given.展开更多
Some classical penalty function algorithms may not always be convergent under big penalty parameters in Matlab software,which makes them impossible to find out an optimal solution to constrained optimization problems....Some classical penalty function algorithms may not always be convergent under big penalty parameters in Matlab software,which makes them impossible to find out an optimal solution to constrained optimization problems.In this paper,a novel penalty function(called M-objective penalty function) with one penalty parameter added to both objective and constrained functions of inequality constrained optimization problems is proposed.Based on the M-objective penalty function,an algorithm is developed to solve an optimal solution to the inequality constrained optimization problems,with its convergence proved under some conditions.Furthermore,numerical results show that the proposed algorithm has a much better convergence than the classical penalty function algorithms under big penalty parameters,and is efficient in choosing a penalty parameter in a large range in Matlab software.展开更多
文摘In this paper, we study linear static Stac kelberg problems with multiple leaders-followers in which each decision maker wi thin his group may or may not cooperate. An exact penalty function method is dev eloped. The duality gaps of the followers’ problems are appended to the leaders’ objective function with a penalty. The structure leads to the decomposition of the composite problem into a series of linear programmings leading to an efficie nt algorithm. We prove that local optimality is reached for an exact penalty fun ction and illustrate the method with three examples. The model in this paper ext ends the stackelberg leader-follower model.
文摘In the criminal justice system, the criminal execution though is the last part, but with the conviction and sentencing of the system have the same importance. Criminal conviction and sentencing execution is guaranteed to achieve, but also fairness and justice contained in the Criminal Code. In criminal law enforcement issues related to research more deeply refined today, supervision of Criminal changes have also been made to perform individually and have a very important significance. A direct result of the implementation of the activities of Criminal debtor prison of term prison sentences and the way to change the location, and the status of implementation as well as criminal penalties for the personal interests are closely related, and therefore it is a very, important enforcement regime. Under our current legal environment, the high amount of crime, large numbers of people in custody are restdting in criminal arduous tasks. It is coupled with the existing legal provisions for change-flawed execution of supervision that is extremely prone to change in the course of execution carried favoritism, money corruption. Meanwhile, the new introduction of the ＂Criminal Law Amendment eight,＂ is for which the commutation, parole perform content changes made adjustments and changes.But for the first time, it provides for community corrections system officially to be incorporated into China＇ s Criminal Law among but the corresponding lack of prosecutorial oversight and other content specific legal provisions, changes are related to the implementation of community Corrections supervision given probation, parole, probation and other penalties to bring the practical operation of the nroblerns.
基金supported by the National Natural Science Foundation of China under Grant No.10971118the Science foundation of Shandong Province(J10LG04)
文摘For smooth optimization problem with equMity constraints, new continuously differentiable penalty function is derived. It is proved exact in the sense that local optimizers of a nonlinear program are precisely the optimizers of the associated penalty function under some nondegeneracy assumption. It is simple in the sense that the penalty function only includes the objective function and constrained functions, and it doesn＇t include their gradients. This is achieved by augmenting the dimension of the program by a variable that controls the weight of the penalty terms.
基金supported by National Natural Science Foundation of China(Grant Nos.11401124 and 71271021)the Scientific Research Projects for the Introduced Talents of Guizhou University(Grant No.201343)the Key Program of National Natural Science Foundation of China(Grant No.11431002)
文摘Regularized minimization problems with nonconvex, nonsmooth, even non-Lipschitz penalty functions have attracted much attention in recent years, owing to their wide applications in statistics, control,system identification and machine learning. In this paper, the non-Lipschitz ?_p(0 < p < 1) regularized matrix minimization problem is studied. A global necessary optimality condition for this non-Lipschitz optimization problem is firstly obtained, specifically, the global optimal solutions for the problem are fixed points of the so-called p-thresholding operator which is matrix-valued and set-valued. Then a fixed point iterative scheme for the non-Lipschitz model is proposed, and the convergence analysis is also addressed in detail. Moreover,some acceleration techniques are adopted to improve the performance of this algorithm. The effectiveness of the proposed p-thresholding fixed point continuation(p-FPC) algorithm is demonstrated by numerical experiments on randomly generated and real matrix completion problems.
基金supported by the National Science Foundation of China under Grant No.71171150the National Natural Science Foundation of ChinaTian Yuan Foundation under Grant No.11226226
文摘For ill-posed bilevel programming problem,the optimistic solution is always the best decision for the upper level but it is not always the best choice for both levels if the authors consider the model's satisfactory degree in application.To acquire a more satisfying solution than the optimistic one to realize the two levels' most profits,this paper considers both levels' satisfactory degree and constructs a minimization problem of the two objective functions by weighted summation.Then,using the duality gap of the lower level as the penalty function,the authors transfer these two levels problem to a single one and propose a corresponding algorithm.Finally,the authors give an example to show a more satisfying solution than the optimistic solution can be achieved by this algorithm.
基金supported by the National Natural Science Foundation of China(Grant No.51375251)the National Basic Research Program("973"Program)(Grant No.2013CB035400)of China
文摘The guide-weight method is introduced to solve the topology optimization problems of thermoelastic structures in this paper.First,the solid isotropic microstructure with penalization(SIMP)with different penalty factors is selected as a material interpolation model for the thermal and mechanical fields.The general criteria of the guide-weight method is then presented.Two types of iteration formulas of the guide-weight method are applied to the topology optimization of thermoelastic structures,one of which is to minimize the mean compliance of the structure with material constraint,whereas the other one is to minimize the total weight with displacement constraint.For each type of problem,sensitivity analysis is conducted based on SIMP model.Finally,four classical 2-dimensional numerical examples and a 3-dimensional numerical example considering the thermal field are selected to perform calculation.The factors that affect the optimal topology are discussed,and the performance of the guide-weight method is tested.The results show that the guide-weight method has the advantages of simple iterative formula,fast convergence and relatively clear topology result.
基金This project is supported by National Natural Science Foundation of China （10971118） and the Science foundation of Shandong Province（2008BS10003）
文摘In this paper, we give a solving approach based on a logarithmic-exponential multiplier penalty function for the constrained minimization problem. It is proved exact in the sense that the global optimizers of a nonlinear problem are precisely the global optimizers of the logarithmic-exponential multiplier penalty problem.
基金supported by the National Natural Science Foundation of China under Grant Nos.10971118, 10701047 and 10901096the Natural Science Foundation of Shandong Province under Grant Nos. ZR2009AL019 and BS2010SF010
文摘For the semi-infinite programming （SIP） problem, the authors first convert it into an equivalent nonlinear programming problem with only one inequality constraint by using an integral function, and then propose a smooth penalty method based on a class of smooth functions. The main feature of this method is that the global solution of the penalty function is not necessarily solved at each iteration, and under mild assumptions, the method is always feasible and efficient when the evaluation of the integral function is not very expensive. The global convergence property is obtained in the absence of any constraint qualifications, that is, any accumulation point of the sequence generated by the algorithm is the solution of the SIP. Moreover, the authors show a perturbation theorem of the method and obtain several interesting results. Furthermore, the authors show that all iterative points remain feasible after a finite number of iterations under the Mangasarian-Fromovitz constraint qualification. Finally, numerical results are given.
基金supported by the National Natural Science Foundation of China under Grant No.11271329
文摘Some classical penalty function algorithms may not always be convergent under big penalty parameters in Matlab software,which makes them impossible to find out an optimal solution to constrained optimization problems.In this paper,a novel penalty function(called M-objective penalty function) with one penalty parameter added to both objective and constrained functions of inequality constrained optimization problems is proposed.Based on the M-objective penalty function,an algorithm is developed to solve an optimal solution to the inequality constrained optimization problems,with its convergence proved under some conditions.Furthermore,numerical results show that the proposed algorithm has a much better convergence than the classical penalty function algorithms under big penalty parameters,and is efficient in choosing a penalty parameter in a large range in Matlab software.
