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Optimality conditions for nonlinear semidefinite programming via squared slack variables

Bruno F. Lourenco(flourenco.b.aa***at***m.titech.ac.jp)
Ellen H. Fukuda(ellen***at***i.kyoto-u.ac.jp)
Masao Fukushima(fuku***at***nanzan-u.ac.jp)

Abstract: In this work, we derive second-order optimality conditions for nonlinear semidefinite programming (NSDP) problems, by reformulating it as an ordinary nonlinear programming problem using squared slack variables. We first consider the correspondence between Karush-Kuhn-Tucker points and regularity conditions for the general NSDP and its reformulation via slack variables. Then, we obtain a pair of "no-gap" second-order optimality conditions that are essentially equivalent to the ones already considered in the literature. We conclude with the analysis of some computational prospects of the squared slack variables approach for NSDP.

Keywords: Nonlinear semidefinite programming, squared slack variables, optimality conditions, second-order conditions

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 2: Nonlinear Optimization


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Entry Submitted: 12/16/2015
Entry Accepted: 12/16/2015
Entry Last Modified: 12/16/2015

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