一类非凸不可微规划的算法

讨论一类带非凸不可微函数约束的非凸不可微规划的求解,提出一种基于分枝定界技巧的算法,该算法具有全局收敛性．     

一类非凸不可微规划的算法

讨论一类带非凸不可微函数约束的非凸不可微规划的求解．提出一种基于分枝定界技巧的算法,该算法具有全局收敛性。     

不可微规划

本文的第一部分对于讨论不可微规划所必需的非光滑分析中有关广义导数、次微分和最优性条件的一些基本结果做了概述;第二部分介绍了几种处理不可微问题的方法和技巧,其中包括光滑化方法、外近似方法、线性化方法和将可微问题的算法推广到不可微问题的技巧。     

不可微规划的极大熵不动点算法

本文将极大熵逼近方法和不动点计算方法有机地结合,提出了一种不可微规划计算方法．该方法同样也适用于求解可微规划,而后给出了该方法的收敛性     

不可微D．C．规划的最优性条件

不可微Ｄ．Ｃ．规划的最优性条件李忠民，边欣（天津大学）（天津教育学院）在非凸不可微规划中，有两种重要类型：ｓｕｐ｛ｇ（ｘ）：。６Ｃ｝，：Ｔ。ｉｎｆ｛ｇ（ｘ）一ｈ（ｘ）：。ｅＣ｝，》其中ｑ、ｈ：Ｒ，＋Ｒ是不可微的凸函数，Ｃ是Ｒ·上的ＩＷ凸集。文【１］在...     

不可微规划的一个积分下降算法

第一部分 不可微规划一般可写成如下形式 min{f(x)|g(x)≤0,x∈R~n},其中f为R~n→R的函数,g=(g_1,…,g_m),每个g_i也是R~n→R的函数.本文研究不带约束的不可微规划min{f(x)},在第一部分介绍不可微规划的一些基本概念以及两种主要的算法思想,这两种思想将应用在本文的算法设计中.第二部分给出算法采用的基本积分概念,引理及有关结果.第三、四部分分别给出算出S1和S2.     

不可微多目标规划问题的最优性条件

本文在文献[1]的基础上,建立了不可微多目标规划的一个最优性条件。     

一类复合不可微规划的二阶最优性条件

本文给出了一类复合不可微规划的二阶最优性条件,拓广了R·Fletcher的结论.     

广义分式规划中的鞍点存在性定理

利用向量值广义凸函数等概念,讨论了一类不可微广义分布式规划的Lagrange函数,在适当条件下,证明了广义分式规划中的鞍点存在性定理。     

一类复合不可微规划的信赖域算法

提出了求解带线性的束的复不可微规划的信赖域算法,并证明了它的收敛性。     

弧拟凸函数的性质

本文对文［１］中引入的弧拟凸函数的性质做了进一步研究，找出了弧拟凸性与严格弧拟凸性及下半连续性之间的联系。同时，还对拟线性函数的性质做了进一步研究。     

Characterization of R-Evenly Quasiconvex Functions

A function defined on a locally convex space is called evenly quasiconvex if its level sets are intersections of families of open half-spaces. Furthermore, if the closures of these open halfspaces do not contain the origin, then the function is called R-evenly quasiconvex. In this note, R-evenly quasiconvex functions are characterized as those evenly-quasiconvex functions that satisfy a certain simple relation with their lower semicontinuous hulls.     

Quasidifferentiability of nonsmooth quasiconvex functions

The paper deals with nonsmooth quasiconvex functions and develops a quasidifferential analysis for this class of functions. Therefore, in terms of sub and superdifferentials, first order approximations of the functions are derived, optimality conditions are stated and directions of descent (either simple feasible or of steepest descent) are determined. Moreover, a relation among positively homogeneous convex and quasiconvex functions is established     

关于局部极小值点为整体极小值点的函数的一点注记

本引进了一种广义严格拟凸函数的定义,给出了它的一个刻画,证明 了局部极小值点为整体极小值点的函数与本定义的广义严格拟凸函数的等价性。     

Subdifferential calculus for a quasiconvex function with generator

Recently, we discussed optimality conditions for quasiconvex programming by introducing ‘Q-subdifferential’, which is a notion of differential of quasiconvex functions. In this paper, we investigate basic and fundamental properties of the Q-subdifferential. Especially, we show results of a chain rule for composition with non-decreasing functions, monotonicity of the Q-subdifferential, mean-value theorem, a sufficient condition for a global minimizer for quasiconvex programming, and the calculus of the Q-subdifferential of the supremum of quasiconvex functions.     

Three kinds of generalized convexity

This paper gives some properties of quasiconvex, strictly quasiconvex, and strongly quasiconvex functions. Relationships between them are discussed.This research was supported in part by the National Natural Science Foundation of China. The author would like to thank Professor M. Avriel for valuable comments about this paper.     

Set containment characterization with strict and weak quasiconvex inequalities

Dual characterizations of the containment of a convex set, defined by infinite quasiconvex constraints, in an evenly convex set, and in a reverse convex set, defined by infinite quasiconvex constraints, are provided. Notions of quasiconjugate for quasiconvex functions, λ-quasiconjugate and λ-semiconjugate, play important roles to derive the characterizations of the set containments.     

拟凸函数判别准则的一个注记

我们在上半连续的条件下,给出了拟凸函数的一个新的判别准则,即：凸集上的一个上半连续函数是拟凸的充分必要条件是这个函数是中间拟凸的。     

Set containment characterization for quasiconvex programming

Dual characterizations of containment of a convex set, defined by quasiconvex constraints, in a convex set, and in a reverse convex set, defined by a quasiconvex constraint, are provided. Notions of quasiconjugate for quasiconvex functions, H-quasiconjugate and R-quasiconjugate, play important roles to derive characterizations of the set containments.