Elementary Optimality Conditions for Nonlinear SDPs

Florian Jarre ()
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Florian Jarre: University of Düsseldorf

Chapter Chapter 16 in Handbook on Semidefinite, Conic and Polynomial Optimization, 2012, pp 455-470 from Springer

Abstract: Abstract An increasing number of recent applications rely on the solution of nonlinear semidefinite programs. First and second order optimality conditions for nonlinear programs are widely known today. This chapter generalizes these optimality conditions to nonlinear semidefinite programs, highlighting some parallels and some differences. It starts by discussing a constraint qualification for both programs. First order optimality conditions are presented for the case where this constraint qualification is satisfied. For the second order conditions, in addition, strict complementarity is assumed.

Keywords: Tangential Cone; Constraint Qualification; Strict Complementarity; Critical Cone; Order Optimality Condition (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-0769-0_16

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