A primal-dual interior point method for nonlinear semidefinite programming

被引：40

作者：

Yamashita, Hiroshi ^{[2
]}

Yabe, Hiroshi ^{[1
]}

Harada, Kouhei ^{[2
]}

机构：

[1] Tokyo Univ Sci, Fac Sci, Dept Math Informat Sci, Shinjuku Ku, Tokyo 1628601, Japan

[2] Math Syst Inc, Shinjuku Ku, Tokyo 1600022, Japan

来源：

MATHEMATICAL PROGRAMMING | 2012年 / 135卷 / 1-2期

基金：

日本学术振兴会;

关键词：

Nonlinear semidefinite programming; Primal-dual interior point method; Barrier penalty function; Primal-dual merit function; Global convergence; ROBUST-CONTROL; CONVERGENCE;

D O I：

10.1007/s10107-011-0449-z

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

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.

引用

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页码：89 / 121

页数：33

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