QSDPNAL swMATH ID: 18799 Software Authors: Li, X.D., Sun, D.F., Toh. K.-C. Description: QSDPNAL: a two-phase augmented Lagrangian method for convex quadratic semidefinite programming. In this paper, we present a two-phase augmented Lagrangian method, called QSDPNAL, for solving convex quadratic semidefinite programming (QSDP) problems with constraints consisting of a large number of linear equality and inequality constraints, a simple convex polyhedral set constraint, and a positive semidefinite cone constraint. A first order algorithm which relies on the inexact Schur complement based decomposition technique is developed in QSDPNAL-Phase I with the aim of solving a QSDP problem to moderate accuracy or using it to generate a reasonably good initial point for the second phase. In QSDPNAL-Phase II, we design an augmented Lagrangian method (ALM) wherein the inner subproblem in each iteration is solved via inexact semismooth Newton based algorithms. Simple and implementable stopping criteria are designed for the ALM. Moreover, under mild conditions, we are able to establish the rate of convergence of the proposed algorithm and prove the R-(super)linear convergence of the KKT residual. In the implementation of QSDPNAL, we also develop efficient techniques for solving large scale linear systems of equations under certain subspace constraints. More specifically, simpler and yet better conditioned linear systems are carefully designed to replace the original linear systems and novel shadow sequences are constructed to alleviate the numerical difficulties brought about by the crucial subspace constraints. Extensive numerical results for various large scale QSDPs show that our two-phase algorithm is highly efficient and robust in obtaining accurate solutions. The software reviewed as part of this submission was given the DOI (Digital Object Identifier) doi:10.5281/zenodo.1206980. Homepage: http://www.math.nus.edu.sg/~mattohkc/papers/QSDPNAL.pdf Source Code: https://github.com/optXuDLi/QSDPNAL Related Software: SDPNAL+; SDPT3; QSDP; Matlab; QAPLIB; Gurobi; CPLEX; LIBSVM; Biq Mac; SeDuMi; Mosek; PPROJ; iFEM; CVXGEN; ECOS; SPOT; UCI-ml; PDCO; DIMACS; OEIS Cited in: 37 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year QSDPNAL: a two-phase augmented Lagrangian method for convex quadratic semidefinite programming. Zbl 1411.90213Li, Xudong; Sun, Defeng; Toh, Kim-Chuan 2018 all top 5 Cited by 55 Authors 15 Sun, Defeng 15 Toh, Kim Chuan 7 Li, Xudong 5 Chen, Liang 3 Cui, Ying 3 Liang, Ling 3 Song, Xiaoliang 3 Xiao, Yunhai 3 Yu, Bo 2 Ahmadi, Amir Ali 2 Chen, Zixuan 2 Ding, Chao 2 Hu, ShengLong 2 Zhao, Xinyuan 1 Bi, Shujun 1 Chang, Xiaokai 1 Chen, Bo 1 Chen, Mingshuai 1 Chen, Xiaotong 1 de Klerk, Etienne 1 Ding, Yanyun 1 Hall, Georgina 1 Huang, Pengfei 1 Jin, Zhengfen 1 Katoen, Joost-Pieter 1 Lam, Xin Yee 1 Li, Donghui 1 Li, Guoyin 1 Li, Jia 1 Li, Min 1 Li, Qingna 1 Lin, Youyicun 1 Liu, Sanyang 1 Liu, Yong-Jin 1 Majumdar, Anirudha 1 Marron, James Stephen 1 Padovani, Cristina 1 Pan, Shaohua 1 Porcelli, Margherita 1 Qian, Yitian 1 Sun, Jie 1 Tang, Peipei 1 Wang, Chengjing 1 Wang, Qiuye 1 Wang, Shuangyue 1 Wu, Zhongming 1 Xue, Bai 1 Yang, Lei 1 Yang, Liuqin 1 Yang, Qingzhi 1 Yang, Yuning 1 Zhai, Fengzhen 1 Zhan, Naijun 1 Zhang, Ning 1 Zhang, Xuping all top 5 Cited in 18 Serials 7 SIAM Journal on Optimization 5 Mathematical Programming. Series A. Series B 5 Computational Optimization and Applications 3 Asia-Pacific Journal of Operational Research 2 Journal of Optimization Theory and Applications 2 Mathematical Programming Computation 1 ACM Transactions on Mathematical Software 1 Calcolo 1 Journal of Computational and Applied Mathematics 1 Mathematics of Operations Research 1 Journal of Global Optimization 1 Journal of Mathematical Imaging and Vision 1 Computational and Applied Mathematics 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Journal of Machine Learning Research (JMLR) 1 Journal of Industrial and Management Optimization 1 Journal of Computational and Graphical Statistics 1 SIAM Journal on Applied Algebra and Geometry all top 5 Cited in 14 Fields 31 Operations research, mathematical programming (90-XX) 21 Numerical analysis (65-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 5 Computer science (68-XX) 2 Algebraic geometry (14-XX) 2 Systems theory; control (93-XX) 1 Field theory and polynomials (12-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Convex and discrete geometry (52-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistics (62-XX) 1 Mechanics of deformable solids (74-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year