In this paper, we establish a theoretical framework of path-following interior point al- gorithms for the linear complementarity problems over symmetric cones (SCLCP) with the Cartesian P*(κ)-property, a weaker condi...In this paper, we establish a theoretical framework of path-following interior point al- gorithms for the linear complementarity problems over symmetric cones (SCLCP) with the Cartesian P*(κ)-property, a weaker condition than the monotonicity. Based on the Nesterov-Todd, xy and yx directions employed as commutative search directions for semidefinite programming, we extend the variants of the short-, semilong-, and long-step path-following algorithms for symmetric conic linear programming proposed by Schmieta and Alizadeh to the Cartesian P*(κ)-SCLCP, and particularly show the global convergence and the iteration complexities of the proposed algorithms.展开更多
Mehrotra's recent suggestion of a predictor corrector variant of primal dual interior point method for linear programming is currently the interior point method of choice for linear programming. In this work t...Mehrotra's recent suggestion of a predictor corrector variant of primal dual interior point method for linear programming is currently the interior point method of choice for linear programming. In this work the authors give a predictor corrector interior point algorithm for monotone variational inequality problems. The algorithm was proved to be equivalent to a level 1 perturbed composite Newton method. Computations in the algorithm do not require the initial iteration to be feasible. Numerical results of experiments are presented.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
We design a grey wolf optimizer hybridized with an interior point algorithm to correct a faulty antenna array. If a single sensor fails, the radiation power pattern of the entire array is disturbed in terms of sidelob...We design a grey wolf optimizer hybridized with an interior point algorithm to correct a faulty antenna array. If a single sensor fails, the radiation power pattern of the entire array is disturbed in terms of sidelobe level（SLL） and null depth level（NDL）, and nulls are damaged and shifted from their original locations. All these issues can be solved by designing a new fitness function to reduce the error between the preferred and expected radiation power patterns and the null limitations. The hybrid algorithm has been designed to control the array＇s faulty radiation power pattern. Antenna arrays composed of 21 sensors are used in an example simulation scenario. The MATLAB simulation results confirm the good performance of the proposed method, compared with the existing methods in terms of SLL and NDL.展开更多
A tumor is referred to as“intracranial hard neoplasm”if it grows near the brain or central spinal vessel(neoplasm).In certain cases,it is possible that the responsible cells are neurons situated deep inside the brai...A tumor is referred to as“intracranial hard neoplasm”if it grows near the brain or central spinal vessel(neoplasm).In certain cases,it is possible that the responsible cells are neurons situated deep inside the brain’s structure.This article discusses a strategy for halting the progression of brain tumor.A precise and accurate analytical model of brain tumors is the foundation of this strategy.It is based on an algorithm known as kill chain interior point(KCIP),which is the result of a merger of kill chain and interior point algorithms,as well as a precise and accurate analytical model of brain tumors.The inability to obtain a clear picture of tumor cell activity is the biggest challenge in this endeavor.Based on the motion of swarm robots,which are considered a subset of artificial intelligence,this article proposes a new notion of this kind of behavior,which may be used in various situations.The KCIP algorithm that follows is used in the analytical model to limit the development of certain cell types.According to the findings,it seems that different KCIP speed ratios are beneficial in preventing the development of brain tumors.It is hoped that this study will help researchers better understand the behavior of brain tumors,so as to develop a new drug that is effective in eliminating the tumor cells.展开更多
The paper presents a technique for solving the binary linear programming model in polynomial time. The general binary linear programming problem is transformed into a convex quadratic programming problem. The convex q...The paper presents a technique for solving the binary linear programming model in polynomial time. The general binary linear programming problem is transformed into a convex quadratic programming problem. The convex quadratic programming problem is then solved by interior point algorithms. This settles one of the open problems of whether P = NP or not. The worst case complexity of interior point algorithms for the convex quadratic problem is polynomial. It can also be shown that every liner integer problem can be converted into binary linear problem.展开更多
redictor-corrector algorithm for linear programming, proposed by Mizuno et al. [1], becomes the best-known in the interior point methods. In this paper it is modified and then extended to solving a class of convex sep...redictor-corrector algorithm for linear programming, proposed by Mizuno et al. [1], becomes the best-known in the interior point methods. In this paper it is modified and then extended to solving a class of convex separable programming problems.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 10671010, 70841008)
文摘In this paper, we establish a theoretical framework of path-following interior point al- gorithms for the linear complementarity problems over symmetric cones (SCLCP) with the Cartesian P*(κ)-property, a weaker condition than the monotonicity. Based on the Nesterov-Todd, xy and yx directions employed as commutative search directions for semidefinite programming, we extend the variants of the short-, semilong-, and long-step path-following algorithms for symmetric conic linear programming proposed by Schmieta and Alizadeh to the Cartesian P*(κ)-SCLCP, and particularly show the global convergence and the iteration complexities of the proposed algorithms.
文摘Mehrotra's recent suggestion of a predictor corrector variant of primal dual interior point method for linear programming is currently the interior point method of choice for linear programming. In this work the authors give a predictor corrector interior point algorithm for monotone variational inequality problems. The algorithm was proved to be equivalent to a level 1 perturbed composite Newton method. Computations in the algorithm do not require the initial iteration to be feasible. Numerical results of experiments are presented.
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.
基金supported by the Ministry of Higher Education(MOHE)the Research Management Centre(RMC)+2 种基金the School of Postgraduate Studies(SPS)the Communication Engineering Department,the Faculty of Electrical Engineering(FKE)Universiti T¨ekùnolóogi Malaysia(UTM)Johor Bahru(Nos.12H09 and 03E20tan)
文摘We design a grey wolf optimizer hybridized with an interior point algorithm to correct a faulty antenna array. If a single sensor fails, the radiation power pattern of the entire array is disturbed in terms of sidelobe level（SLL） and null depth level（NDL）, and nulls are damaged and shifted from their original locations. All these issues can be solved by designing a new fitness function to reduce the error between the preferred and expected radiation power patterns and the null limitations. The hybrid algorithm has been designed to control the array＇s faulty radiation power pattern. Antenna arrays composed of 21 sensors are used in an example simulation scenario. The MATLAB simulation results confirm the good performance of the proposed method, compared with the existing methods in terms of SLL and NDL.
文摘A tumor is referred to as“intracranial hard neoplasm”if it grows near the brain or central spinal vessel(neoplasm).In certain cases,it is possible that the responsible cells are neurons situated deep inside the brain’s structure.This article discusses a strategy for halting the progression of brain tumor.A precise and accurate analytical model of brain tumors is the foundation of this strategy.It is based on an algorithm known as kill chain interior point(KCIP),which is the result of a merger of kill chain and interior point algorithms,as well as a precise and accurate analytical model of brain tumors.The inability to obtain a clear picture of tumor cell activity is the biggest challenge in this endeavor.Based on the motion of swarm robots,which are considered a subset of artificial intelligence,this article proposes a new notion of this kind of behavior,which may be used in various situations.The KCIP algorithm that follows is used in the analytical model to limit the development of certain cell types.According to the findings,it seems that different KCIP speed ratios are beneficial in preventing the development of brain tumors.It is hoped that this study will help researchers better understand the behavior of brain tumors,so as to develop a new drug that is effective in eliminating the tumor cells.
文摘The paper presents a technique for solving the binary linear programming model in polynomial time. The general binary linear programming problem is transformed into a convex quadratic programming problem. The convex quadratic programming problem is then solved by interior point algorithms. This settles one of the open problems of whether P = NP or not. The worst case complexity of interior point algorithms for the convex quadratic problem is polynomial. It can also be shown that every liner integer problem can be converted into binary linear problem.
文摘redictor-corrector algorithm for linear programming, proposed by Mizuno et al. [1], becomes the best-known in the interior point methods. In this paper it is modified and then extended to solving a class of convex separable programming problems.
