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Author:

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

Indexed by:

EI Scopus SCIE

Abstract:

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.

Keyword:

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

Author Community:

  • [ 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

Reprint Author's Address:

  • 赵欣苑

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

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Source :

OPTIMIZATION METHODS & SOFTWARE

ISSN: 1055-6788

Year: 2020

Issue: 1

Volume: 35

Page: 87-115

2 . 2 0 0

JCR@2022

ESI Discipline: COMPUTER SCIENCE;

ESI HC Threshold:132

Cited Count:

WoS CC Cited Count: 48

SCOPUS Cited Count: 50

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 9

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