Local and superlinear convergence of a primal-dual interior point method for nonlinear semidefinite programming

Hiroshi Yamashita(hymsi.co.jp)
Hiroshi Yabe(yabers.kagu.tus.ac.jp)

Abstract: In this paper, we consider a primal-dual interior point method for solving nonlinear semidefinite programming problems. We propose primal-dual interior point methods based on the unscaled and scaled Newton methods, which correspond to the AHO, HRVW/KSH/M and NT search directions in linear SDP problems. We analyze local behavior of our proposed methods and show their local and superlinear convergence properties.

Keywords: nonlinear semidefinite programming, primal-dual interior point method, local and superlinear convergence

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

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Technical report, January 26, 2009, Mathematical Systems Inc./Department of Mathematical Information Science, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan.

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Entry Submitted: 08/08/2009
Entry Accepted: 08/08/2009
Entry Last Modified: 08/08/2009

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