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.
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页码：89 / 121
页数：33
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