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Error Bounds of Two Smoothing Approximations for Semi-infinite Minimax Problems 认领 引用 被引量：1
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作者 Hong-xia Yin 《Acta Mathematicae Applicatae Sinica》 SCIE 2009年第4期685-696,共12页
In the paper we investigate smoothing method for solving semi-infinite minimax problems. Not like most of the literature in semi-infinite minimax problems which are concerned with the continuous time version（i.e., th... In the paper we investigate smoothing method for solving semi-infinite minimax problems. Not like most of the literature in semi-infinite minimax problems which are concerned with the continuous time version（i.e., the one dimensional semi-infinite minimax problems）, the primary focus of this paper is on multi- dimensional semi-infinite minimax problems. The global error bounds of two smoothing approximations for the objective function are given and compared. It is proved that the smoothing approximation given in this paper can provide a better error bound than the existing one in literature. 展开更多
关键词 Semi-infinite minimax problem smoothing method aggregate function error bound polynomial interpolation
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Necessary Optimality Conditions for Multi-Objective Semi-Infinite Variational Problem 认领 引用 被引量：1
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作者 Bharti Sharma Promila Kumar 《American Journal of Operations Research》 2016年第1期36-43,共8页
In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These co... In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These conditions are responsible for the development of duality theory which is an extremely important feature for any class of problems, but the literature available so far lacks these necessary optimality conditions for the stated problem. A lemma is also proved to find the topological dual of  as it is required to prove the desired result. 展开更多
关键词 Semi-Infinite Variational Problem Efficient Solution Necessary Optimality Conditions
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INTERVAL ADJUSTABLE ENTROPY ALGORITHM FOR A CLASS OF UNCONSTRAINED DISCRETE MINIMAX PROBLEMS 认领 引用 被引量：6
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作者 LiSubei CaoDexin +1 位作者 WangHaijun DengKazhong 《Applied Mathematics(A Journal of Chinese Universities)》 2004年第1期37-43,共7页
In this paper,a class of unconstrained discrete minimax problems is described,in which the objective functions are in C 1.The paper deals with this problem by means of taking the place of maximum entropy function with... In this paper,a class of unconstrained discrete minimax problems is described,in which the objective functions are in C 1.The paper deals with this problem by means of taking the place of maximum entropy function with adjustable entropy function.By constructing an interval extension of adjustable entropy function an d some region deletion test rules,a new interval algorithm is presented.The rele vant properties are proven.The minimax value and the localization of the minimax points of the problem can be obtained by this method. This method can overcome the flow problem in the maximum entropy algorithm.Both theoretical and numerica l results show that the method is reliable and efficient. 展开更多
关键词 discrete minimax problem adjustable entropy function interval algorithm .
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Three-Dimensional Thermal-Stress Analysis of Semi-infinite Transversely Isotropic Composites 认领 引用
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作者 TOKOVYY Yuriy BOIKO Dmytro GAO Cunfa 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2021年第1期18-28,共11页
By making use of the direct integration method,an exact analysis of the general three-dimensional thermoelasticity problem is performed for the case of a transversely isotropic homogeneous half-space subject to local ... By making use of the direct integration method,an exact analysis of the general three-dimensional thermoelasticity problem is performed for the case of a transversely isotropic homogeneous half-space subject to local thermal and force loadings.The material plane of isotropy is assumed to be parallel to the limiting surface of the halfspace.By reducing the original thermoelasticity equations to the governing ones for individual stress-tensor components,the effect of material anisotropy in the stress field is analyzed with regard to the feasibility requirement,i.e.,the finiteness of the stress field at a distance from the disturbed area.As a result,the solution is constructed in the form of explicit analytical dependencies on the force and thermal loadings for various kinds of transversely isotropic materials and agrees with the basic principles of the continua mechanics.The solution can be efficiently used as a benchmark one for the direct computation of temperature and thermal stresses in transversely isotropic semi-infinite domains,as well as for the verification of solutions constructed by different means. 展开更多
关键词 three-dimensional problem analytical solution transversely isotropic composites semi-infinite model force and thermal loadings finite stress distributions
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Interval Algorithm for Inequality Constrained Discrete Minimax Problems 认领 引用 被引量：3
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作者 叶帅民 曹德欣 《International Journal of Mining Science and Technology》 CAS 1999年第1期92-96,共5页
An interval algorlthm for inequality coustrained discrete minimax problems is described, in which the constrained and objective functions are C1 functions. First, based on the penalty function methods, we trans form t... An interval algorlthm for inequality coustrained discrete minimax problems is described, in which the constrained and objective functions are C1 functions. First, based on the penalty function methods, we trans form this problem to unconstrained optimization. Second, the interval extensions of the penalty functions and the test rules of region deletion are discussed. At last, we design an interval algorithm with the bisection rule of Moore. The algorithm provides bounds on both the minimax value and the localization of the minimax points of the problem. Numerical results show that algorithm is reliable and efficiency. 展开更多
关键词 interval algorithm discrete minimax problem inequality constrained penalty function
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Nonsmooth Equations of K-T Systems for a Constrained Minimax Problem 认领 引用 被引量：5
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作者 Gao Yan School of Management, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China 《Journal of Systems Engineering and Electronics》 EI 2003年第2期31-35,共5页
Using K-T optimality condition of nonsmooth optimization, we establish two equivalent systems of the nonsmooth equations for the constrained minimax problem directly. Then generalized Newton methods are applied to sol... Using K-T optimality condition of nonsmooth optimization, we establish two equivalent systems of the nonsmooth equations for the constrained minimax problem directly. Then generalized Newton methods are applied to solve these systems of the nonsmooth equations. Thus a new approach to solving the constrained minimax problem is developed. 展开更多
关键词 Optimization Minimax problems Nonsmooth equations Generalized Newton methods.
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Solving constrained minimax problem via nonsmooth equations method 认领 引用
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作者 郭修霞 《Journal of Coal Science & Engineering(China)》 2004年第1期109-111,共3页
A new nonsmooth equations model of constrained minimax problem was de-rived. The generalized Newton method was applied for solving this system of nonsmooth equations system. A new algorithm for solving constrained min... A new nonsmooth equations model of constrained minimax problem was de-rived. The generalized Newton method was applied for solving this system of nonsmooth equations system. A new algorithm for solving constrained minimax problem was established. The local superlinear and quadratic convergences of the algorithm were discussed. 展开更多
关键词 nonsmooth equations minimax problem generalized newton method nonsmooth optimization
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A Nonmonotone Filter Method for Minimax Problems 认领 引用 被引量：2
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作者 Qi Zhao Nan Guo 《Applied Mathematics》 2011年第11期1372-1377,共6页
In this paper, we propose a modified trust-region filter method algorithm for Minimax problems, which based on the framework of SQP-filter method and associated with the technique of nonmonotone method. We use the SQP... In this paper, we propose a modified trust-region filter method algorithm for Minimax problems, which based on the framework of SQP-filter method and associated with the technique of nonmonotone method. We use the SQP subproblem to acquire an attempt step, and use the filter to weigh the effect of the attempt step so as to avoid using penalty function. The algorithm uses the Lagrange function as a merit function and the nonmonotone filter to improve the effect of the algorithm. Under some mild conditions, we prove the global convergence. 展开更多
关键词 Minimax Problem Nonmonotone Global Convergence Filter Methods
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AN ITERATIVE METHOD FOR THE MINIMAX PROBLEM 认领 引用
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作者 祁立群 孙文瑜 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 1995年第2期237-239,共3页
In this paper a class of iterative methods for the minimax problem i; proposed.We present a sequence of the extented linear-quadratic programming (ELQP) problems as subproblems of the original minimal problem and solv... In this paper a class of iterative methods for the minimax problem i; proposed.We present a sequence of the extented linear-quadratic programming (ELQP) problems as subproblems of the original minimal problem and solve the ELQP problem iteratively.The locally linear and su-perlinear convergence results of the algorithm are established. 展开更多
关键词 minimax problem mathematical programming linear-quadratic programming convergence
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An Alternating Proximal Gradient Algorithm for Nonsmooth Nonconvex-Linear Minimax Problems with Coupled Linear Constraints 认领 引用
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作者 Hui-Ling Zhang Zi Xu 《Journal of the Operations Research Society of China》 EI CSCD 2026年第2期502-520,共19页
In this paper,we propose an alternating proximal gradient algorithm for solving nonsmooth nonconvex-linear minimax problems with coupled linear constraints,which have attracted wide attention in machine learning,signa... In this paper,we propose an alternating proximal gradient algorithm for solving nonsmooth nonconvex-linear minimax problems with coupled linear constraints,which have attracted wide attention in machine learning,signal processing and many other fields in recent years.The iteration complexity of the proposed algorithm is proved to be O(ε-3)to reach anε-stationary point.To our knowledge,this is the first algorithm with iteration complexity guarantee for solving nonsmooth nonconvex-linear minimax problems with coupled linear constraints. 展开更多
关键词 Minimax optimization problem Alternating proximal gradient algorithm Iteration complexity Machine learning
一类非凸-非凹极小极大问题的方差缩减梯度下降上升算法 认领 引用
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作者 王子琦 王军霖 徐姿 《运筹学学报（中英文）》 CSCD 北大核心 2026年第1期197-206,共10页
考虑一类随机非凸-非凹的极小极大问题,假设目标函数关于里层变量y满足Polyak-Lojasiewicz(PL)条件,我们也称这类问题为NC-PL极小极大问题。本文提出了一种用于求解随机NC-PL极小极大问题的方差缩减的梯度下降上升(VRGDA)算法,且证明了... 考虑一类随机非凸-非凹的极小极大问题,假设目标函数关于里层变量y满足Polyak-Lojasiewicz(PL)条件,我们也称这类问题为NC-PL极小极大问题。本文提出了一种用于求解随机NC-PL极小极大问题的方差缩减的梯度下降上升(VRGDA)算法,且证明了该算法解得ε-稳定点的迭代复杂度为O(ε-3)。这也是目前求解一般化随机NC-PL问题复杂度最好的一阶算法。 展开更多
关键词 极小极大优化问题 机器学习 方差缩减方法
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求解约束Minimax问题一种改进的可行下降束方法 认领 引用 被引量：2
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作者 唐春明 梁玲 丁何斌 《广西大学学报（自然科学版）》 CAS 北大核心 2018年第2期839-847,共9页
通过引入一个新型下降测试准则,提出了求解不等式约束极大极小(Minimax)问题一种改进的可行下降束方法。该方法不仅克服了现有方法下降参数选取的困难,而且简化了理论分析。算法具备全局收敛性,且数值试验结果具有明显优势。
关键词 不等式约束 极大极小问题 束方法 下降测试准则 全局收敛性
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约束Minimax问题的SQP-Filter算法及收敛性 认领 引用 被引量：2
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作者 谢亚君 马昌凤 《西华大学学报（自然科学版）》 CAS 2011年第6期61-64,共4页
提出了一个求解带等式和不等式约束的Minimax问题的SQP-Filter算法,每步通过求解2个二次规划子问题来得到搜索方向,并沿该方向做线搜索。该算法避免了较难的罚因子的选取,克服了Maratos效应,并在适当的假设条件下,得到了算法的全局收敛性。
关键词 运筹学 Minimax问题 SQP-Filter算法 全局收敛性
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一类Minimax分式规划问题的迭代算法 认领 引用 被引量：3
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作者 申培萍 陈晓 《河南师范大学学报（自然科学版）》 CAS 北大核心 2018年第1期16-22,共7页
对一类Minimax分式规划问题(MFP)提出一个迭代算法.首先通过引进变量和指数变换,将问题(MFP)等价转化为问题(Q),然后利用代数-几何平均不等式以及合适的转化过程,将等价问题(Q)压缩为凸规划问题(Q).从而根据选择不同的点所对应的压缩问... 对一类Minimax分式规划问题(MFP)提出一个迭代算法.首先通过引进变量和指数变换,将问题(MFP)等价转化为问题(Q),然后利用代数-几何平均不等式以及合适的转化过程,将等价问题(Q)压缩为凸规划问题(Q).从而根据选择不同的点所对应的压缩问题(Q),将原问题的求解过程转化为求解一系列的凸规划问题.数值实验表明算法是可行有效的. 展开更多
关键词 Minimax问题 凸规划 迭代算法
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基于Minimax目标函数的多宗量稳态热传导反演 认领 引用 被引量：1
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作者 薛齐文 杨海天 《大连交通大学学报》 CAS 2007年第1期11-14,共4页
基于Minimax目标函数,建立了求解稳态热传导反问题优化新模型,并应用BFGS算法进行求解.同时考虑了非均质的影响,对热物性参数和边界条件进行多宗量组合反演,并对信息误差和初值作了初步探讨,数值验证给出了令人满意的结果.
关键词 极大极小 反问题 热传导 多宗量
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一类无约束离散minimax问题的区间斜率方法 认领 引用 被引量：1
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作者 吴健波 储丹华 《青岛大学学报（自然科学版）》 CAS 2009年第2期27-33,共7页
进一步讨论了一类由一阶连续可微函数构成的无约束离散minimax问题。利用区间斜率方法和区域二分原则,构造了极大函数的区间扩张和无解区域删除检验原则,建立了区间斜率算法;对算法进行了数值实验,并给出了数值算例,结果表明:该方法可... 进一步讨论了一类由一阶连续可微函数构成的无约束离散minimax问题。利用区间斜率方法和区域二分原则,构造了极大函数的区间扩张和无解区域删除检验原则,建立了区间斜率算法;对算法进行了数值实验,并给出了数值算例,结果表明:该方法可以同时求出问题的最优值和全部全局最优解,是有效和可靠的。 展开更多
关键词 minimax问题 区间斜率 全局解
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A PENALTY FUNCTION METHOD FOR THE PRINCIPAL-AGENT PROBLEM WITH AN INFINITE NUMBER OF INCENTIVE-COMPATIBILITY CONSTRAINTS UNDER MORAL HAZARD 认领 引用
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作者 Jia LIU Xianjia WANG 《Acta Mathematica Scientia》 SCIE CSCD 2021年第5期1749-1763,共15页
In this paper,we propose an iterative algorithm to find the optimal incentive mechanism for the principal-agent problem under moral hazard where the number of agent action profiles is infinite,and where there are an i... In this paper,we propose an iterative algorithm to find the optimal incentive mechanism for the principal-agent problem under moral hazard where the number of agent action profiles is infinite,and where there are an infinite number of results that can be observed by the principal.This principal-agent problem has an infinite number of incentive-compatibility constraints,and we transform it into an optimization problem with an infinite number of constraints called a semi-infinite programming problem.We then propose an exterior penalty function method to find the optimal solution to this semi-infinite programming and illustrate the convergence of this algorithm.By analyzing the optimal solution obtained by the proposed penalty function method,we can obtain the optimal incentive mechanism for the principal-agent problem with an infinite number of incentive-compatibility constraints under moral hazard. 展开更多
关键词 principal-agent problem mechanism design moral hazard semi-infinite programming problem penalty function method
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Existence results for generalized vector equilibrium problems with applications 认领 引用
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作者 杨明歌 黄南京 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2014年第7期913-924,共12页
By a coincidence theorem, some existence theorems of solutions are proved for four types of generalized vector equilibrium problems with moving cones. Applications to the generalized semi-infinite programs with the ge... By a coincidence theorem, some existence theorems of solutions are proved for four types of generalized vector equilibrium problems with moving cones. Applications to the generalized semi-infinite programs with the generalized vector equilibrium constraints under the mild conditions are also given. The results of this paper unify and improve the corresponding results in the previous literature. 展开更多
关键词 generalized vector equilibrium problem generalized semi-infinite program,abstract convex space -map
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Behavior of solution set for bilevel generalized mixed equilibrium problems in topological vector spaces 认领 引用
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作者 丁协平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2014年第7期925-934,共10页
A new bilevel generalized mixed equilibrium problem （BGMEF） is introduced and studied in topological vector spaces. By using a minimax inequality, the existence of solutions and the behavior of solution set for the ... A new bilevel generalized mixed equilibrium problem （BGMEF） is introduced and studied in topological vector spaces. By using a minimax inequality, the existence of solutions and the behavior of solution set for the BGMEP are studied under quite mild conditions. These results are new and generalize some recent results in this field. 展开更多
关键词 generalized mixed equilibrium problem （GMEP） bilevel generalized mixedequilibrium problem （BGMEP） monotonicity minimax inequality topological vectorspace
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Adjustable entropy method for solving convex inequality problem 认领 引用
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作者 Wang Ruopeng 《Journal of Systems Engineering and Electronics》 SCIE EI 2009年第5期1111-1114,共4页
To solve the inequality problem, an adjustable entropy method is proposed. An inequality problem can be transformed into a minimax problem which is nondifferentiable; then an adjustable entropy is used to smooth the m... To solve the inequality problem, an adjustable entropy method is proposed. An inequality problem can be transformed into a minimax problem which is nondifferentiable; then an adjustable entropy is used to smooth the minimax problem. The solution of inequalities can be approached by using a BFGS algorithm of the standard optimization method. Some properties of the new approximate function are presented and then the global convergence are given according to the algorithm. Two numerical examples illustrate that the proposed method is efficient and is superior to the former ones. 展开更多
关键词 operational research optimization adjustable entropy function minimax problem inequality problem.
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