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作者:

Sun, Defeng (Sun, Defeng.) | Toh, Kim-Chuan (Toh, Kim-Chuan.) | Yuan, Yancheng (Yuan, Yancheng.) | Zhao, Xin-Yuan (Zhao, Xin-Yuan.) (学者:赵欣苑)

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EI Scopus SCIE

摘要:

Sdpnal+ is a MATLAB software package that implements an augmented Lagrangian based method to solve large scale semidefinite programming problems with bound constraints. The implementation was initially based on a majorized semismooth Newton-CG augmented Lagrangian method, here we designed it within an inexact symmetric Gauss-Seidel based semi-proximal ADMM/ALM (alternating direction method of multipliers/augmented Lagrangian method) framework for the purpose of deriving simpler stopping conditions and closing the gap between the practical implementation of the algorithm and the theoretical algorithm. The basic code is written in MATLAB, but some subroutines in C language are incorporated via Mex files. We also design a convenient interface for users to input their SDP models into the solver. Numerous problems arising from combinatorial optimization and binary integer quadratic programming problems have been tested to evaluate the performance of the solver. Extensive numerical experiments conducted in [L.Q. Yang, D.F. Sun, and K.C. Toh, SDPNAL+: A majorized semismooth Newton-CG augmented Lagrangian method for semidefinite programming with nonnegative constraints, Math. Program. Comput. 7 (2015), pp. 331-366] show that the proposed method is quite efficient and robust, in that it is able to solve 98.9% of the 745 test instances of SDP problems arising from various applications to the accuracy of in the relative KKT residual.

关键词:

semismooth Newton-CG method Matlab software package augmented Lagrangian Semidefinite programming

作者机构:

  • [ 1 ] [Sun, Defeng]Hong Kong Polytech Univ, Dept Appl Math, Hung Hom, Hong Kong, Peoples R China
  • [ 2 ] [Toh, Kim-Chuan]Natl Univ Singapore, Dept Math, Singapore, Singapore
  • [ 3 ] [Yuan, Yancheng]Natl Univ Singapore, Dept Math, Singapore, Singapore
  • [ 4 ] [Yuan, Yancheng]Natl Univ Singapore, Inst Operat Res & Analyt, Singapore, Singapore
  • [ 5 ] [Zhao, Xin-Yuan]Beijing Univ Technol, Beijing Inst Sci & Engn Comp, Beijing, Peoples R China

通讯作者信息:

  • 赵欣苑

    [Zhao, Xin-Yuan]Beijing Univ Technol, Beijing Inst Sci & Engn Comp, Beijing, Peoples R China

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来源 :

OPTIMIZATION METHODS & SOFTWARE

ISSN: 1055-6788

年份: 2020

期: 1

卷: 35

页码: 87-115

2 . 2 0 0

JCR@2022

ESI学科: COMPUTER SCIENCE;

ESI高被引阀值:132

被引次数:

WoS核心集被引频次: 44

SCOPUS被引频次: 47

ESI高被引论文在榜: 0 展开所有

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