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Existence and Uniquess of H..K..M Search Direction of Primal-Dual Interior Point Algorithm for Quadratic Semtdefinite Programming

Aiwen Wang

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Abstract

This paper extends the interior point algorithm for solving Semidefinite Programming(SDP) to Quadratic Semidefinite Programming(QSDP),especially discussing the generation of search direction.Firstly,we derive the nonlinear equations for the solution of QSDP using Wolfe′s dual theorem.The H..K..M search direction is got by applying Newton method to the equations.Then we prove the existence and uniqueness of the search direction,and give how to compute H.K.M search direction concretely.

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What this paper is about

This paper extends the interior point algorithm for solving Semidefinite Programming(SDP) to Quadratic Semidefinite Programming(QSDP),especially discussing the generation of search direction.Firstly,we derive the nonlinear equations for the solution of QSDP using Wolfe′s dual theorem.The H..K..M search direction is got by applying Newton method to the equations.Then we prove the existence and uniqueness of the search direction,and give how to compute H.K.M search direction concretely.

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Available abstract

This paper extends the interior point algorithm for solving Semidefinite Programming(SDP) to Quadratic Semidefinite Programming(QSDP),especially discussing the generation of search direction.Firstly,we derive the nonlinear equations for the solution of QSDP using Wolfe′s dual theorem.The H..K..M search direction is got by applying Newton method to the equations.Then we prove the existence and uniqueness of the search direction,and give how to compute H.K.M search direction concretely.

Key concepts: Interior point method, Uniqueness, Mathematics, Semidefinite programming, Quadratic programming, Quadratic equation, Dual (grammatical number), Point (geometry)

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Existence and Uniquess of H..K..M Search Direction of Primal-Dual Interior Point Algorithm for Quadratic Semtdefinite Programming — Research Paper | ScholarLens