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Second-Order Variational Analysis in Conic Programming with Applications to Optimality and Stability

Boris Mordukhovich(boris***at***math.wayne.edu)
Jiri Outrata(outrata***at***utia.cas.cz)
Hector Ramirez(hramirez***at***dim.uchile.cl)

Abstract: This paper is devoted to the study of a broad class of problems in conic programming modeled via parameter-dependent generalized equations. In this framework we develop a second-order generalized di erential approach of variational analysis to calculate appropriate derivatives and coderivatives of the corresponding solution maps. These developments allow us to resolve some important issues related to conic programming. They include: veri able conditions for isolated calmness of the considered solution maps, sharp necessary optimality conditions for a class of mathematical programs with equilibrium constraints, and characterizations of tilt-stable local minimizers for cone-constrained problems. The main results obtained in the general conic programming setting are specified for and illustrated by the second-order cone programming.

Keywords: Variational analysis, second-order theory, conic programming, generalized differentiation, optimality conditions, isolated calmness, tilt stability.

Category 1: Convex and Nonsmooth Optimization


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Entry Submitted: 01/02/2013
Entry Accepted: 01/03/2013
Entry Last Modified: 01/02/2013

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