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A primal–dual interior point method for nonlinear semidefinite programming

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Abstract

This paper is concerned with a primal–dual interior point method for solving nonlinear semidefinite programming problems. The method consists of the outer iteration (SDPIP) that finds a KKT point and the inner iteration (SDPLS) that calculates an approximate barrier KKT point. Algorithm SDPLS uses a commutative class of Newton-like directions for the generation of line search directions. By combining the primal barrier penalty function and the primal–dual barrier function, a new primal–dual merit function is proposed. We prove the global convergence property of our method. Finally some numerical experiments are given.

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Authors and Affiliations

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

    Hiroshi Yamashita & Kouhei Harada

  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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  3. Kouhei Harada
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Correspondence to Hiroshi Yabe.

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Yamashita, H., Yabe, H. & Harada, K. A primal–dual interior point method for nonlinear semidefinite programming. Math. Program. 135, 89–121 (2012). https://doi.org/10.1007/s10107-011-0449-z

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  • DOI: https://doi.org/10.1007/s10107-011-0449-z

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