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

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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.

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Authors and Affiliations

  1. Mathematical Systems Inc., 2-4-3, Shinjuku, Shinjuku-ku, Tokyo, 160-0022, Japan

    Hiroshi Yamashita

  2. Department of Mathematical Information Science, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo, 162-8601, Japan

    Hiroshi Yabe

Authors
  1. Hiroshi Yamashita
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  2. Hiroshi Yabe
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Correspondence to Hiroshi Yamashita.

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Yamashita, H., Yabe, H. Local and superlinear convergence of a primal-dual interior point method for nonlinear semidefinite programming. Math. Program. 132, 1–30 (2012). https://doi.org/10.1007/s10107-010-0354-x

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  • DOI: https://doi.org/10.1007/s10107-010-0354-x

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