On the Cones of Tangents with Applications to Mathematical Programming

被引：47

作者：

Bazaraa, M. S. ^{[1
]}

Goode, J. J. ^{[2
]}

Nashed, M. Z. ^{[2
]}

机构：

[1] Georgia Inst Technol, Sch Ind & Syst Engn, Atlanta, GA 30332 USA

[2] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 1974年 / 13卷 / 04期

关键词：

Tangent cones; mathematical programming; in-equality constraints; minimax problems; optimization theorems; constraint qualification;

D O I：

10.1007/BF00934938

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this study, we present a unifying framework for the cones of tangents to an arbitrary set and some of its applications. We highlight the significance of these cones and their polars both from the point of view of differentiability and subdifferentiability theory and the point of view of mathematical programming. This leads to a generalized definition of a subgradient which extends the well-known definition of a subgradient of a convex function to the nonconvex case. As an application, we develop necessary optimality conditions for a min-max problem and show that these conditions are also sufficient under moderate convexity assumptions.

引用

页码：389 / 426

页数：38