SINGLE-DIRECTIONAL PROPERTY OF MULTIVALUED MAPS AND VARIATIONAL SYSTEMS

被引：9

作者：

Aussel, D. ^{[1
]}

Garcia, Y. ^{[2
]}

Hadjisavvas, N. ^{[3
]}

机构：

[1] Univ Perpignan, Dept Math, F-66025 Perpignan, France

[2] Univ Chile, Ctr Modelamiento Matemat, Santiago, Chile

[3] Univ Aegean, Dept Prod & Syst Design Engn, Hermoupolis, Syros, Greece

来源：

SIAM JOURNAL ON OPTIMIZATION | 2009年 / 20卷 / 03期

关键词：

Aubin property; Lipschitz-like property; single-directional property; metric regularity; quasi-monotone map; normal operator; parametric variational systems; METRIC REGULARITY; CONSTRAINT; SETS;

D O I：

10.1137/080735618

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Dontchev and Hager [Math. Oper. Res., 19 (1994), pp. 753-768] have shown that a monotone set-valued map defined from a Banach space to its dual which satisfies the Aubin property around a point (x, y) of its graph is actually single-valued in a neighborhood of x. We prove a result which is the counterpart of the above for quasi-monotone set-valued maps, based on the concept of single-directional property. As applications, we provide sufficient conditions for this single-valued property to hold for the solution map of general variational systems and quasi-variational inequalities. We also investigate the single-directionality property for the normal operator to the sublevel sets of a quasi-convex function.

引用

页码：1274 / 1285

页数：12

共 13 条

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[Anonymous], 2006, GRUNDLEHREN MATH WIS

[2]

ARTACHO FJA, NONLINEAR A IN PRESS

[3]

Aubin J.-P., 1990, Set-Valued Analysis

[4] Quasiconvex programming with locally starshaped constraint region and applications to quasiconvex MPEC [J].