CONVEX FUNCTIONS WITH UNBOUNDED LEVEL SETS AND APPLICATIONS TO DUALITY THEORY

被引：40

作者：

Auslender, A. ^{[1
]}

Cominetti, R. ^{[2
]}

Crouzeix, J. -P. ^{[1
]}

机构：

[1] Univ Blaise Pascal, Dept Appl Math, F-63177 Aubiere, France

[2] Univ Chile, Santiago, Chile

来源：

SIAM JOURNAL ON OPTIMIZATION | 1993年 / 3卷 / 04期

关键词：

convex optimization; duality; inf-compactness; good asymptotic behavior; relaxed constraint qualification; algorithms;

D O I：

10.1137/0803034

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A class of convex functions with unbounded level sets but good behavior at infinity [Analyse non-lingaire, Gauthier-Villars, Paris, 1989, pp. 101-122] is investigated. Characterizations and properties are given. The results are then applied to studying sequential approximation schemes for optimization problems and to duality theory, when the involved functions have unbounded level sets. In particular, the convergence properties of stationary sequences for the dual of a convex program are studied, and methods for associating with it a primal sequence converging to a solution of the primal problem are demonstrated.

引用

页码：669 / 687

页数：19

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