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2016•Journal of Industrial and Management OptimizationOpen access

Semidefinite programming via image space analysis

Shouhong Yang

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Abstract

In this paper, we investigate semidefinite programming by using the image space analysis and present some equivalence between the (regular) linear separation and the saddle points of the Lagrangian functions related to semidefinite programming. Some necessary and sufficient optimality conditions for semidefinite programming are also given under some suitable assumptions. As an application, we obtainsome equivalent characterizations for necessary and sufficient optimality conditions for linear semidefinite programming under Slater assumption.

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What this paper is about

In this paper, we investigate semidefinite programming by using the image space analysis and present some equivalence between the (regular) linear separation and the saddle points of the Lagrangian functions related to semidefinite programming. Some necessary and sufficient optimality conditions for semidefinite programming are also given under some suitable assumptions. As an application, we obtainsome equivalent characterizations for necessary and sufficient optimality conditions for linear semidefinite programming under Slater assumption.

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Available abstract

In this paper, we investigate semidefinite programming by using the image space analysis and present some equivalence between the (regular) linear separation and the saddle points of the Lagrangian functions related to semidefinite programming. Some necessary and sufficient optimality conditions for semidefinite programming are also given under some suitable assumptions. As an application, we obtainsome equivalent characterizations for necessary and sufficient optimality conditions for linear semidefinite programming under Slater assumption.

Key concepts: Semidefinite programming, Semidefinite embedding, Equivalence (formal languages), Mathematics, Linear programming, Mathematical optimization, Large margin nearest neighbor, Second-order cone programming

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