一个对偶问题与对偶性质

本文对非可微凸规划问题建立了一个新的对偶问题 ,并证明其对偶性质 ,如弱对偶性 ,强对偶性及逆对偶性。     

非可微凸规划的对偶问题

文章建立关于非可微凸规划的一个新的对偶问题,它不同于已知的对偶问题,文中证明了弱对偶性及强对偶性。并用Ｌａｇｒａｎｇｅ正则性证明了强对偶性的充要条件。最后,讨论了等式约束的情况。     

E-凸条件下多目标规划的Mond-Weir型对偶研究

本文主要研究E-凸函数的若干性质,引入E-凸多目标规划的定义,建立E-凸多目标规划的Mond-Weir型对偶问题,并在E.凸条件假设下,证明E-凸多目标规划的弱对偶性、直接对偶性及逆对偶性.     

由方向导数表述的对偶问题

本文利用扰动函数的方向导数引进凸规划的一个新的对偶问题，并证明了相应的对偶性．     

G-(F,ρ)凸意义下多目标规划真有效解的对偶性

本文利用文［1］中的有关结果，讨论带等式约束和不等式约束的多目标规划关于Geoffrion真有效解的对偶性，建立了Wolfe及Mond－Weir型对偶问题，并在G－（F，ρ）凸型假设下，证明了弱、强及逆对偶定理．     

多目标无限线性规划的对偶性

本文讨论多目标无限线性规划的对偶性，它将有限多目标的结果推广到了无限信的情形。     

关于非光滑不变凸多目标规划的Wolfe型对偶

本文讨论定义在Banach空间上的,既具有等式约束又具有不等式约束的,非光滑(F,P)不变凸多目标规划的Wolfe对偶性,Mond-Weir型对偶性可类似讨论之。     

关于耦合反应扩散系统解的整体存在性

利用对偶性技巧及Hoelder不等式，证明了一类耦合反应扩散系统解的整体存在性，推广了相关结果．     

一种新的诱导覆盖粗糙集

定义了一种新的诱导覆盖粗糙集,这种定义可以保证其满足对偶性.然后证明了该诱导覆盖粗糙集具备的性质.最后讨论了两种诱导覆盖粗糙集之间的关系.     

非光滑非凸多目标规划的Wolfe型对偶性

本文利用作者提出的某些非凸概念,讨论了非光滑非凸多目标规划的Wolfe型对偶性.     

Multiobjective duality for convex ratios

In this paper we present a duality approach for a multiobjective fractional programming problem. The components of the vector objective function are particular ratios involving the square of a convex function and a positive concave function. Applying the Fenchel-Rockafellar duality theory for a scalar optimization problem associated to the multiobjective primal, a dual problem is derived. This scalar dual problem is formulated in terms of conjugate functions and its structure gives an idea about how to construct a multiobjective dual problem in a natural way. Weak and strong duality assertions are presented.     

Duality for nonconvex absolute value programming and a characterization of linear max-min programs

In this paper a dual problem for nonconvex linear programs with absolute value functionals is constructed by means of a max-min problem involving bivalent variables. A relationship between the classical linear max-min problem and a linear program with absolute value functionals is developed. This program is then used to compute the duality gap between some max-min and min-max linear problems.     

有界整规划中的渐近强非线性对偶

本文提出了一种整数规划中的指数一对数对偶.证明了此指数-对数对偶方法具有的渐近强对偶性质,并提出了不需要进行对偶搜索来解原整数规划问题的方法.特别地,当选取合适的参数和对偶变量时,原整数规划问题的解可以通过解一个非线性松弛问题来得到.对具有整系数目标函数及约束函数的多项式整规划问题,给出了参数及对偶变量的取法.     

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     

Comparison between different duals in multiobjective fractional programming

The present paper is a continuation of [2] where we deal with the duality for a multiobjective fractional optimization problem. The basic idea in [2] consists in attaching an intermediate multiobjective convex optimization problem to the primal fractional problem, using an approach due to Dinkelbach ([6]), for which we construct then a dual problem expressed in terms of the conjugates of the functions involved. The weak, strong and converse duality statements for the intermediate problems allow us to give dual characterizations for the efficient solutions of the initial fractional problem. The aim of this paper is to compare the intermediate dual problem with other similar dual problems known from the literature. We completely establish the inclusion relations between the image sets of the duals as well as between the sets of maximal elements of the image sets.      

Diewert-Crouzeix conjugation for general quasiconvex duality and applications

A complicated factor in quasiconvex duality is the appearance of extra parameters. In order to avoid these extra parameters, one often has to restrict the class of quasiconvex functions. In this paper, by using the Diewert-Crouzeix conjugation, we present a duality without an extra parameter for general quasiconvex minimization problem. As an application, we prove a decentralization by prices for the Von Neumann equilibrium problem.     

Conjugate dual problems in constrained set-valued optimization and applications

In this paper, two conjugate dual problems are proposed by considering the different perturbations to a set-valued vector optimization problem with explicit constraints. The weak duality, inclusion relations between the image sets of dual problems, strong duality and stability criteria are investigated. Some applications to so-called variational principles for a generalized vector equilibrium problem are shown.     

A linear programming approach to solving bilinear programmes

This paper discusses the maximization of a bilinear function over two independent polytopes. The maximization problem is converted into a max—min problem, using duality. This problem is then solved via a sequence of dual linear programmes, whose constraint vectors are successively determined bytth order optima of a master linear programme.