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Variational Analysis of Circular Cone Programs

Jinchuan Zhou(jinchuanzhou***at***163.com)
Jein-Shan Chen(jschen***at***math.ntnu.edu.tw)
Boris S. Mordukhovich(boris***at***math.wayne.edu)

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/coderivatives of the projection operator associated with the circular cone. Then we apply generalized di erentiation and other tools of variational analysis to establish complete characterizations of full and tilt stability of locally optimal solutions to parameterized circular programs.

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

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Linear, Cone and Semidefinite Programming (Other )

Citation:

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Entry Submitted: 02/01/2014
Entry Accepted: 02/02/2014
Entry Last Modified: 02/01/2014

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