This paper presents an efficient method for solving unconstrained semi-infiniteminimax problems and constrained semi-infinite minimax problems and constrainedsemi-infinite problems, in which these two kinds of problem...This paper presents an efficient method for solving unconstrained semi-infiniteminimax problems and constrained semi-infinite minimax problems and constrainedsemi-infinite problems, in which these two kinds of problems are approximated byunconstrained differentible optimization problems. Numerical examples are givento show the high efficiency of the method.展开更多
针对粒子群优化算法易早熟收敛、求解精度低等缺点,提出基于进化能力的多策略粒子群优化算法(multistrategy particle swarm optimization algorithm based on evolution ability)。将粒子按照适应值变化方向分为进步粒子和停退粒子。...针对粒子群优化算法易早熟收敛、求解精度低等缺点,提出基于进化能力的多策略粒子群优化算法(multistrategy particle swarm optimization algorithm based on evolution ability)。将粒子按照适应值变化方向分为进步粒子和停退粒子。对于进步粒子按照原始进化策略更新,保留原算法的优点。对于停退粒子进一步根据粒子活性分为暂时停退粒子和长久停退粒子,针对暂时停退的粒子,减小对个体历史速度的依赖甚至向相反方向学习,针对长久停退粒子,根据粒子的适应值优劣采用不同的进化策略,提高全局寻优能力。同时,设计一种带随机波动的惯性权重,使粒子在算法后期仍然具有跳出当前区域的能力,利于全局搜索。通过与其他算法在10个测试函数不同维度上的优化结果对比表明,该算法无论对低维还是高维问题求解的收敛速度和求解精度均有优势。将EAMSPSO算法应用于半无限规划问题的求解,实验结果表明,该算法可以用于半无限规划问题的求解,且具有优势。展开更多
A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research t...A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research topics in mathematical programming. In this paper, we discuss a fairly large number of paramet- ric duality results under various generalized （η,ρ）-invexity assumptions for a semi-infinite minmax fractional programming problem.展开更多
The convergence of the maximum entropy method of nonsmooth semi-infinite programmings is proved, and the stability and the strong stability of the method are discussed.
This paper obtains sufficient optimality conditions for a nonlinear nondifferentiable multiobjective semi-infinite programming problem involving generalized(C,α,ρ,d)-convex functions.The authors formulate Mond-Weir-...This paper obtains sufficient optimality conditions for a nonlinear nondifferentiable multiobjective semi-infinite programming problem involving generalized(C,α,ρ,d)-convex functions.The authors formulate Mond-Weir-type dual model for the nonlinear nondifferentiable multiobjective semiinfinite programming problem and establish weak,strong and strict converse duality theorems relating the primal and the dual problems.展开更多
In this paper,we study optimality conditions of approximate solutions for nonsmooth semi-infinite programming problems.Three new classes of functions,namelyε-pseudoconvex functions of type I and type II andε-quasico...In this paper,we study optimality conditions of approximate solutions for nonsmooth semi-infinite programming problems.Three new classes of functions,namelyε-pseudoconvex functions of type I and type II andε-quasiconvex functions are introduced,respectively.By utilizing these new concepts,sufficient optimality conditions of approximate solutions for the nonsmooth semi-infinite programming problem are established.Some examples are also presented.The results obtained in this paper improve the corresponding results of Son et al.(J Optim Theory Appl 141:389–409,2009).展开更多
In this paper, we discuss a large number of sets of global parametric sufficient optimality conditions under various generalized （η,ρ）-invexity assumptions for a semi-infinite minmax fractional programming problem.
In this paper, we study optimal value functions of generalized semi-infinite min-max programming problems on a noncompact set. Directional derivatives and subdifferential characterizations of optimal value functions a...In this paper, we study optimal value functions of generalized semi-infinite min-max programming problems on a noncompact set. Directional derivatives and subdifferential characterizations of optimal value functions are given. Using these properties,we establish first order optimality conditions for unconstrained generalized semi-infinite programming problems.展开更多
The aim of this article is to discuss an asymptotic approximation model and its convergence for the minimax semi-infinite programming problem. An asymptotic surrogate constraints method for the minimax semi-infinite p...The aim of this article is to discuss an asymptotic approximation model and its convergence for the minimax semi-infinite programming problem. An asymptotic surrogate constraints method for the minimax semi-infinite programming problem is presented by making use of two general discrete approximation methods. Simultaneously, the consistence and the epi-convergence of the asymptotic approximation problem are discussed.展开更多
文摘This paper presents an efficient method for solving unconstrained semi-infiniteminimax problems and constrained semi-infinite minimax problems and constrainedsemi-infinite problems, in which these two kinds of problems are approximated byunconstrained differentible optimization problems. Numerical examples are givento show the high efficiency of the method.
文摘针对粒子群优化算法易早熟收敛、求解精度低等缺点,提出基于进化能力的多策略粒子群优化算法(multistrategy particle swarm optimization algorithm based on evolution ability)。将粒子按照适应值变化方向分为进步粒子和停退粒子。对于进步粒子按照原始进化策略更新,保留原算法的优点。对于停退粒子进一步根据粒子活性分为暂时停退粒子和长久停退粒子,针对暂时停退的粒子,减小对个体历史速度的依赖甚至向相反方向学习,针对长久停退粒子,根据粒子的适应值优劣采用不同的进化策略,提高全局寻优能力。同时,设计一种带随机波动的惯性权重,使粒子在算法后期仍然具有跳出当前区域的能力,利于全局搜索。通过与其他算法在10个测试函数不同维度上的优化结果对比表明,该算法无论对低维还是高维问题求解的收敛速度和求解精度均有优势。将EAMSPSO算法应用于半无限规划问题的求解,实验结果表明,该算法可以用于半无限规划问题的求解,且具有优势。
文摘A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research topics in mathematical programming. In this paper, we discuss a fairly large number of paramet- ric duality results under various generalized （η,ρ）-invexity assumptions for a semi-infinite minmax fractional programming problem.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 19871049 and 19731001).
文摘The convergence of the maximum entropy method of nonsmooth semi-infinite programmings is proved, and the stability and the strong stability of the method are discussed.
文摘This paper obtains sufficient optimality conditions for a nonlinear nondifferentiable multiobjective semi-infinite programming problem involving generalized(C,α,ρ,d)-convex functions.The authors formulate Mond-Weir-type dual model for the nonlinear nondifferentiable multiobjective semiinfinite programming problem and establish weak,strong and strict converse duality theorems relating the primal and the dual problems.
基金This work was partially supported by the National Natural Science Foundation of China(Nos.11471059 and 11671282)the Chongqing Research Program of Basic Research and Frontier Technology(Nos.cstc2014jcyjA00037,cstc2015jcyjB00001 and cstc2014jcyjA00033)+2 种基金the Education Committee Project Research Foundation of Chongqing(Nos.KJ1400618 and KJ1400630)the Program for University Innovation Team of Chongqing(No.CXTDX201601026)the Education Committee Project Foundation of Bayu Scholar.
文摘In this paper,we study optimality conditions of approximate solutions for nonsmooth semi-infinite programming problems.Three new classes of functions,namelyε-pseudoconvex functions of type I and type II andε-quasiconvex functions are introduced,respectively.By utilizing these new concepts,sufficient optimality conditions of approximate solutions for the nonsmooth semi-infinite programming problem are established.Some examples are also presented.The results obtained in this paper improve the corresponding results of Son et al.(J Optim Theory Appl 141:389–409,2009).
文摘In this paper, we discuss a large number of sets of global parametric sufficient optimality conditions under various generalized （η,ρ）-invexity assumptions for a semi-infinite minmax fractional programming problem.
基金The authors thank Prof.J.Y.Han,Dr.Lian Shujun and the referees for their valuable suggestion.This work was parially supported by the National Natural Science Foundation of China(Grants No.10171055 and 10171118)the Excellent Young Teachers Program of M0E,P.R.C.the Research Committee of the Hong Kong Polytechnic University.
文摘In this paper, we study optimal value functions of generalized semi-infinite min-max programming problems on a noncompact set. Directional derivatives and subdifferential characterizations of optimal value functions are given. Using these properties,we establish first order optimality conditions for unconstrained generalized semi-infinite programming problems.
基金Supported by the National Key Basic Research Special Fund(2003CB415200)the National Science Foundation(70371032 and 60274048)the Doctoral Foundation of the Ministry of Education(20020486035)
文摘The aim of this article is to discuss an asymptotic approximation model and its convergence for the minimax semi-infinite programming problem. An asymptotic surrogate constraints method for the minimax semi-infinite programming problem is presented by making use of two general discrete approximation methods. Simultaneously, the consistence and the epi-convergence of the asymptotic approximation problem are discussed.
