A primal-dual interior point method for nonlinear semidefinite programming

被引：43

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

页码：89 / 121

页数：33

共 50 条

[41] Improving the performance of primal-dual interior-point method in inverse conductivity problems [J].

Javaherian, Ashkan ;

Movafeghi, Amir ;

Faghihi, Reza ;

Yahaghi, Effat .

TURKISH JOURNAL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCES, 2015, 23 (02) :459-479

[42] Convergence conditions and Krylov subspace-based corrections for primal-dual interior-point method [J].

Mehrotra, S ;

Li, ZF .

SIAM JOURNAL ON OPTIMIZATION, 2005, 15 (03) :635-653

[43] A Globally and Superlinearly Convergent Primal-dual Interior Point Method for General Constrained Optimization [J].

Li, Jianling ;

Lv, Jian ;

Jian, Jinbao .

NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2015, 8 (03) :313-335

[44] A new feasible descent primal-dual interior point algorithm for nonlinear inequality constrained optimization [J].

Jian, Jin-bao ;

Pan, Hua-qin .

APPLIED MATHEMATICAL MODELLING, 2010, 34 (07) :1952-1963

[45] LDLT DIRECTION INTERIOR POINT METHOD FOR SEMIDEFINITE PROGRAMMING [J].

Raghunathan, Arvind U. ;

Biegler, Lorenz T. .

SIAM JOURNAL ON OPTIMIZATION, 2018, 28 (01) :693-734

[46] Research on Spot Price Based on Predictor-corrector Primal-dual Interior Point Method [J].

Huang, Qincheng ;

Zhou, Yurong .

INTERNATIONAL CONFERENCE ON ELECTRICAL AND CONTROL ENGINEERING (ICECE 2015), 2015, :68-74

[47] A primal-dual interior point method to implicitly update Gurson-Tvergaard-Needleman model [J].

Shintaku, Yuichi ;

Inaoka, Tatsuhiko ;

Terada, Kenjiro .

COMPUTATIONAL MECHANICS, 2024, 74 (05) :1037-1054

[48] A Derivative-Free Regularized Primal-Dual Interior-Point Algorithm for Constrained Nonlinear Least Squares Problems [J].

Chen, Xi ;

Fan, Jinyan .

JOURNAL OF SCIENTIFIC COMPUTING, 2025, 103 (02)

[49] DC-based security constraints formulation: A perspective of primal-dual interior point method [J].

Bao, Zhiyuan ;

Wan, Yujian ;

Hu, Zechun ;

Mujeeb, Asad .

ELECTRIC POWER SYSTEMS RESEARCH, 2024, 228

[50] A dynamic large-update primal-dual interior-point method for linear optimization [J].

Peng, JM ;

Terlaky, T .

OPTIMIZATION METHODS & SOFTWARE, 2002, 17 (06) :1077-1104

← 1 2 3 4 5 →