Variational analysis and full stability of optimal solutions to constrained and minimax problems Dedicated to Enzo Mitidieri in honor of his 60th birthday

Boris S. Mordukhovich; M. Ebrahim Sarabi

doi:10.1016/j.na.2014.10.013

Variational analysis and full stability of optimal solutions to constrained and minimax problems Dedicated to Enzo Mitidieri in honor of his 60th birthday

Boris S. Mordukhovich^*
, M. Ebrahim Sarabi

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

The main goal of this paper is to develop applications of advanced tools of first-order and second-order variational analysis and generalized differentiation to the fundamental notion of full stability of local minimizers of general classes of constrained optimization and minimax problems. In particular, we derive second-order characterizations of full stability and investigate its relationships with other notions of stability for parameterized conic programs and minimax problems. Furthermore, the developed variational approach allows us to largely unify and provide new self-contained proofs of some quite recent results in this direction for problems of constrained optimization with ^C2-smooth data.

Original language	English
Pages (from-to)	36-53
Number of pages	18
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	121
DOIs	https://doi.org/10.1016/j.na.2014.10.013
State	Published - 1 Jul 2015

Bibliographical note

Publisher Copyright:
© 2014 Elsevier Ltd. All rights reserved.

Keywords

Constrained parametric optimization
Full stability of local minimizers
Graphical derivative
Minimax problem
Second-order subdifferentials
Strong regularity
Variational analysis

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2014.10.013

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title = "Variational analysis and full stability of optimal solutions to constrained and minimax problems Dedicated to Enzo Mitidieri in honor of his 60th birthday",

abstract = "The main goal of this paper is to develop applications of advanced tools of first-order and second-order variational analysis and generalized differentiation to the fundamental notion of full stability of local minimizers of general classes of constrained optimization and minimax problems. In particular, we derive second-order characterizations of full stability and investigate its relationships with other notions of stability for parameterized conic programs and minimax problems. Furthermore, the developed variational approach allows us to largely unify and provide new self-contained proofs of some quite recent results in this direction for problems of constrained optimization with C2-smooth data.",

keywords = "Constrained parametric optimization, Full stability of local minimizers, Graphical derivative, Minimax problem, Second-order subdifferentials, Strong regularity, Variational analysis",

author = "Mordukhovich, \{Boris S.\} and Sarabi, \{M. Ebrahim\}",

year = "2015",

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doi = "10.1016/j.na.2014.10.013",

language = "English",

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T1 - Variational analysis and full stability of optimal solutions to constrained and minimax problems Dedicated to Enzo Mitidieri in honor of his 60th birthday

AU - Mordukhovich, Boris S.

AU - Sarabi, M. Ebrahim

PY - 2015/7/1

Y1 - 2015/7/1

N2 - The main goal of this paper is to develop applications of advanced tools of first-order and second-order variational analysis and generalized differentiation to the fundamental notion of full stability of local minimizers of general classes of constrained optimization and minimax problems. In particular, we derive second-order characterizations of full stability and investigate its relationships with other notions of stability for parameterized conic programs and minimax problems. Furthermore, the developed variational approach allows us to largely unify and provide new self-contained proofs of some quite recent results in this direction for problems of constrained optimization with C2-smooth data.

AB - The main goal of this paper is to develop applications of advanced tools of first-order and second-order variational analysis and generalized differentiation to the fundamental notion of full stability of local minimizers of general classes of constrained optimization and minimax problems. In particular, we derive second-order characterizations of full stability and investigate its relationships with other notions of stability for parameterized conic programs and minimax problems. Furthermore, the developed variational approach allows us to largely unify and provide new self-contained proofs of some quite recent results in this direction for problems of constrained optimization with C2-smooth data.

KW - Constrained parametric optimization

KW - Full stability of local minimizers

KW - Graphical derivative

KW - Minimax problem

KW - Second-order subdifferentials

KW - Strong regularity

KW - Variational analysis

UR - https://www.scopus.com/pages/publications/84941421871

U2 - 10.1016/j.na.2014.10.013

DO - 10.1016/j.na.2014.10.013

M3 - Article

AN - SCOPUS:84941421871

SN - 0362-546X

VL - 121

SP - 36

EP - 53

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

ER -

Variational analysis and full stability of optimal solutions to constrained and minimax problems Dedicated to Enzo Mitidieri in honor of his 60th birthday

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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