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On Duality Theory for Non-Convex Semidefinite Programming

Wenyu Sun(wysun***at***njnu.edu.cn)
Chengjin Li(chengjin98298***at***sina.com)
Raimundo Sampaio(raimundo.sampaio***at***pucpr.br)

Abstract: In this paper, with the help of convex-like function, we discuss the duality theory for nonconvex semidefinite programming. Our contributions are: duality theory for the general nonconvex semidefinite programming when Slater's condition holds; perfect duality for a special case of the nonconvex semidefinite programming for which Slater's condition fails. We point out that the results of [2] can be regarded as a special case of our result.

Keywords: semidefinite programming, duality, convex-like function, invex function, perfect duality

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

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Technical Report Optim-10, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, China. December/2007.

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Entry Submitted: 11/15/2010
Entry Accepted: 11/15/2010
Entry Last Modified: 11/15/2010

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