QSDPNAL
swMATH ID:  18799 
Software Authors:  Li, X.D., Sun, D.F., Toh. K.C. 
Description:  QSDPNAL: a twophase augmented Lagrangian method for convex quadratic semidefinite programming. In this paper, we present a twophase 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 QSDPNALPhase 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 QSDPNALPhase 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 twophase 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; UCIml; PDCO; DIMACS; OEIS 
Cited in:  37 Documents 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

QSDPNAL: a twophase augmented Lagrangian method for convex quadratic semidefinite programming. Zbl 1411.90213 Li, Xudong; Sun, Defeng; Toh, KimChuan 
2018

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Cited by 55 Authors
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Cited in 18 Serials
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