凸规划的一个对偶问题

1引言考虑标准的非可微凸规划问题     

非凸规划的对偶问题极值

本文对非凸规划的对偶问题的目标函数极值给出一个表达式 ,从而得出对偶间隙 ,使用的方法是扰动函数的凸色 ,而不使用任何有关凸性的假定     

关于宏观经济的凸二次规划模型

本文运用凸二次规划理论，通过引入价格变量建立观经济的凸二次规划模型．并指出在社会主义市场经济中企业、产业、国家可以同时达到最优．     

凸二次-线性双层规划的共轭对偶及其性质

研究具有一般形式的凸二次-线性双层规划问题。讨论了这类双层规划问题的DC规划等价形式,利用DC规划共轭对偶理论,提出了凸二次-线性双层规划的共轭对偶规划,并给出相应的对偶性质。     

一类多目标Lipschitz规划的对偶定理

Lipschitz函数定义了广义本性伪凸的概念,建立了多目标Lipschitz规划的Mond-Weir型对偶和Wolfe型对偶,证明了原规划与对偶规划之间的对偶定理。     

非凸异分母分式多目标规划解的充分条件及对偶定理

指出了文[6]中的一个错误，基于不变凸性，对异分母分式多目标规划进行了讨论．在简单的正交假设下，给出了一系列解的充分条件，并建立了Mond－Weir型对偶定理．     

一类值型双层凸规划的Johri一般对偶

本文首先给出一类特殊的值型凸二次双层规划一其下层子规划只含有线性约束(简记为VBCP)；然后证明了一般形式的VBCP可以等价变换为非增值型凸二次双层规划的形式；最后给出该类双层规划VBCP的Johri对偶规划及其对偶性质．     

求解随机凸规划概率约束问题的对偶算法

1引言随机规划中的概率约束问题在工程和管理中有广泛的应用.因为问题中包含非线性的概率约束,它们的求解非常困难.如果目标函数是线性的,问题的求解就比较容易.给出了一个求解随机线性规划概率约束问题的综述.原-对偶算法和切平面算法是比较有效的.在本文中,我们讨论随机凸规划概率约束问题:     

一致不变凸多目标规划的有效性条件和对偶性

作者对多目标规划引进一致不变凸的概念,用来综合规划所涉及函数的不变凸性,而不是用单个函数的不变凸性.考虑了涉及这样函数的多目标规划解的有效性和Mond-Weir对偶性.     

一类二层凸规划的对偶二层规划

本文讨论上层目标函数以下层子系统目标函数的最优值作为反馈的一类二层凸规划的对偶规划问题 ,在构成函数满足凸连续可微等条件的假设下 ,建立了二层凸规划的 Lagrange对偶二层规划 ,并证明了基本对偶定理 .     

Duality of Unary Convex Functions Programming

Most nonliner programming problems consist of functions which are sums of unary,convexfunctions of linear fuctions.In this paper.we derive the duality forms of the unary oonvex optimization,and these technuqucs are applied to the geometric programming and minimum discrimination informationproblems.     

集函数多目标分式规划的最优性和广义凸对偶性

本文讨论了集函数多目标（分母不同）分式规划，给出了Ｇｅｏｆｆｒｉｏｎ正常有效解的必要和充分条件，并讨论了关于有效解的广义凸对偶理论．     

Fenchel-Lagrange Duality Versus Geometric Duality in Convex Optimization

We present a new duality theory to treat convex optimization problems and we prove that the geometric duality used by Scott and Jefferson in different papers during the last quarter of century is a special case of it. Moreover, weaker sufficient conditions to achieve strong duality are considered and optimality conditions are derived. Next, we apply our approach to some problems considered by Scott and Jefferson, determining their duals. We give weaker sufficient conditions to achieve strong duality and the corresponding optimality conditions. Finally, posynomial geometric programming is viewed also as a particular case of the duality approach that we present. Communicated by V. F. Demyanov The first author was supported in part by Gottlieb Daimler and Karl Benz Stiftung 02-48/99. The second author was supported in part by Karl und Ruth Mayer Stiftung.     

带有极值函数的多目标双层规划问题的对偶

For a multiobjective bilevel programming problem(P) with an extremal-value function,its dual problem is constructed by using the Fenchel-Moreau conjugate of the functions involved.Under some convexity and monotonicity assumptions,the weak and strong duality assertions are obtained.     

A Dual Parametrization Method for Convex Semi-Infinite Programming

We formulate convex semi-infinite programming problems in a functional analytic setting and derive optimality conditions and several duality results, based on which we develop a computational framework for solving convex semi-infinite programs.     

Strong Duality for Generalized Convex Optimization Problems

In this paper, strong duality for nearly-convex optimization problems is established. Three kinds of conjugate dual problems are associated to the primal optimization problem: the Lagrange dual, Fenchel dual, and Fenchel-Lagrange dual problems. The main result shows that, under suitable conditions, the optimal objective values of these four problems coincide. The first author was supported in part by Gottlieb Daimler and Karl Benz Stiftung 02-48/99. This research has been performed while the second author visited Chemnitz University of Technology under DAAD (Deutscher Akademischer Austauschdienst) Grant A/02/12866. Communicated by T. Rapcsák     

Duality Theorems of Multiobjective Programming for a Class of Generalized Convex Functions

1.DefinitionsDefinition1.AfunctionalF(x)inthespaceVCE"issaidtobeasublinearfunctionalifforx,yeV,andor20,Inparticular,F(0)=0.Letop(x)beadifferentiablerealfunctiononasetCCEd.ForagivensublinearfunctionFandafunctionp:CxC-EIIp(x,u)/0(x/u),themoregeneralgeneralizedconvexfunctioncanbedefinedasthefollwing:Definition2.op(x)issaidtobe(F,p)--invarialltconvexfunctiononCifforxl,xZECDefinition3.op(x)issaidtobe(F,P)--invariantquasiconvexfunctiononCifforal,xZECthatis,Definition4.op(x)issaidtobe(F,…     

球约束凸二次规划的一个新算法

首先利用Lagrange对偶 ,将球约束凸二次规划问题转化为无约束优化问题 ,然后运用单纯形法求解无约束优化问题 ,从而获得原问题的最优解     

Generalized Convex Disjunctive Programming: Nonlinear Convex Hull Relaxation

Generalized Disjunctive Programming (GDP) has been introduced recently as an alternative to mixed-integer programming for representing discrete/continuous optimization problems. The basic idea of GDP consists of representing these problems in terms of sets of disjunctions in the continuous space, and logic propositions in terms of Boolean variables. In this paper we consider GDP problems involving convex nonlinear inequalities in the disjunctions. Based on the work by Stubbs and Mehrotra [21] and Ceria and Soares [6], we propose a convex nonlinear relaxation of the nonlinear convex GDP problem that relies on the convex hull of each of the disjunctions that is obtained by variable disaggregation and reformulation of the inequalities. The proposed nonlinear relaxation is used to formulate the GDP problem as a Mixed-Integer Nonlinear Programming (MINLP) problem that is shown to be tighter than the conventional big-M formulation. A disjunctive branch and bound method is also presented, and numerical results are given for a set of test problems.