Variational analysis of circular cone programs

Jinchuan Zhou; Jein Shah Chen; Boris S. Mordukhovich

doi:10.1080/02331934.2014.951043

Variational analysis of circular cone programs

Jinchuan Zhou, Jein Shah Chen, Boris S. Mordukhovich^*

^*Corresponding author for this work

Department of Mathematics

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

17 Citations (Scopus)

Abstract

This paper conducts variational analysis of circular programs, which form a new class of optimization problems in nonsymmetric conic programming, important for optimization theory and its applications. First, we derive explicit formulas in terms of the initial problem data to calculate various generalized derivatives/co-derivatives of the projection operator associated with the circular cone. Then we apply generalized differentiation and other tools of variational analysis to establish complete characterizations of full and tilt stability of locally optimal solutions to parameterized circular programs.

Original language	English
Pages (from-to)	113-147
Number of pages	35
Journal	Optimization
Volume	64
Issue number	1
DOIs	https://doi.org/10.1080/02331934.2014.951043
Publication status	Published - 2015 Jan 2

Keywords

circular cone
conic programming
full and tilt stability
generalized differentiation
optimization
projection operator
second-order cone
variational analysis

ASJC Scopus subject areas

Control and Optimization
Management Science and Operations Research
Applied Mathematics

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N2 - This paper conducts variational analysis of circular programs, which form a new class of optimization problems in nonsymmetric conic programming, important for optimization theory and its applications. First, we derive explicit formulas in terms of the initial problem data to calculate various generalized derivatives/co-derivatives of the projection operator associated with the circular cone. Then we apply generalized differentiation and other tools of variational analysis to establish complete characterizations of full and tilt stability of locally optimal solutions to parameterized circular programs.

AB - This paper conducts variational analysis of circular programs, which form a new class of optimization problems in nonsymmetric conic programming, important for optimization theory and its applications. First, we derive explicit formulas in terms of the initial problem data to calculate various generalized derivatives/co-derivatives of the projection operator associated with the circular cone. Then we apply generalized differentiation and other tools of variational analysis to establish complete characterizations of full and tilt stability of locally optimal solutions to parameterized circular programs.

KW - circular cone

KW - conic programming

KW - full and tilt stability

KW - generalized differentiation

KW - optimization

KW - projection operator

KW - second-order cone

KW - variational analysis

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Variational analysis of circular cone programs

Abstract

Keywords

ASJC Scopus subject areas

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