QPA swMATH ID: 4296 Software Authors: Gould, Nicholas I.M.; Toint, Philippe L. Description: An iterative working-set method for large-scale nonconvex quadratic programming We consider a working-set method for solving large-scale quadratic programming problems for which there is no requirement that the objective function be convex. The methods are iterative at two levels, one level relating to the selection of the current working set, and the second due to the method used to solve the equality-constrained problem for this working set. par A preconditioned conjugate gradient method is used for this inner iteration, with the preconditioner chosen especially to ensure feasibility of the iterates. The preconditioner is updated at the conclusion of each outer iteration to ensure that this feasibility requirement persists. The well-known equivalence between the conjugate-gradient and Lanczos methods is exploited when finding directions of negative curvature. par Details of an implementation – the Fortran 90 package QPA in the forthcoming GALAHAD library – are given. Homepage: http://www.galahad.rl.ac.uk/download.html Dependencies: GALAHAD Keywords: quadratic programming; nonconvex; large-scale; active-set method; preconditioning; conjugate gradient method; Lanczos methods; Fortran 90 package QPA; GALAHAD library Related Software: MA57; SNOPT; qpOASES; SQOPT; GALAHAD; HSL; COPS; ve08; Ipopt; LANCELOT; CUTEst; ZQPCVX; QPSchur; SifDec; CUTEr; L-BFGS; L-BFGS-B; TRON; QP; blockSQP Cited in: 20 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year An iterative working-set method for large-scale nonconvex quadratic programming. Zbl 1012.65054Gould, Nicholas I. M.; Toint, Philippe L. 2002 all top 5 Cited by 39 Authors 3 Gill, Philip E. 3 Gould, Nicholas Ian Mark 3 Wong, Elizabeth 2 Robinson, Daniel P. 2 Toint, Philippe L. 1 Achtziger, Wolfgang 1 Brillout, Angelo 1 Curtis, Frank E. 1 Dai, Meizhong 1 Forsgren, Anders 1 Friedlander, Michael P. 1 Ginzburg, Jonathan 1 Goldfarb, Donald 1 Golovkins, Marats 1 Gould, Nick I. M. 1 Gouveia, Maria Celeste 1 Han, Zheng 1 Janka, Dennis 1 Kirches, Christian 1 Kröning, Daniel 1 Leyffer, Sven 1 Orban, Dominique 1 Puystjens, Roland 1 Ruegg, Henri 1 Rümmer, Philipp 1 Sager, Sebastian 1 Sain, Ildikó 1 Schmidt, David P. 1 Scott, Jennifer A. 1 Sim, Kwang Mong 1 Stolpe, Mathias 1 Thompson, Richard J. 1 Tolstoĭ, Valeriĭ Nikolaevich 1 Wächter, Andreas 1 Wahl, Thomas 1 Wen, Zaiwen 1 Wong, Pui Tak 1 Yin, Wotao 1 Zhang, Yin all top 5 Cited in 12 Serials 2 Computational Optimization and Applications 2 SIAM Journal on Scientific Computing 2 Mathematical Programming Computation 1 Journal of Computational Physics 1 Letters in Mathematical Physics 1 ACM Transactions on Mathematical Software 1 Applied Numerical Mathematics 1 Journal of Logic and Computation 1 Linear Algebra and its Applications 1 Mathematical Programming. Series A. Series B 1 SIAM Journal on Optimization 1 Acta Numerica all top 5 Cited in 12 Fields 10 Operations research, mathematical programming (90-XX) 9 Numerical analysis (65-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 3 Mathematical logic and foundations (03-XX) 2 Computer science (68-XX) 2 Quantum theory (81-XX) 1 General algebraic systems (08-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Associative rings and algebras (16-XX) 1 Nonassociative rings and algebras (17-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) Citations by Year