ZQPCVX
On the quadratic programming algorithm of Goldfarb and Idnani. Two implementations of the algorithm of D. Goldfarb and A. Idnani [Math. Program. 27, 1-33 (1983; Zbl 0537.90081)] for convex quadratic programming are considered. A pathological example shows that the faster one can be unstable, but numerical testing on some difficult problems indicates that both implementations give excellent accuracy. Therefore the author has provided for general use a Fortran subroutine [”ZQPCVX: a Fortran subroutine for convex, quadratic programming”, Report DAMTP/1983/NA17, Dept. Appl. Math. Theor. Phys., Univ. of Cambridge (1983)] that applies the faster implementation. This subroutine is compared with two widely available quadratic programming subroutines that employ feasible point methods, namely QPSOL [see P. E. Gill, W. Murray, M. A. Saunders and M. H. Wright, ”User’s guide for SOL/QPSOL: A Fortran package for quadratic programming”, Report SOL 83-7, Systems Optim. Lab., Rept. Oper. Res., Stanford Univ. (1983)] and VEO2A [see R. Fletcher, ”A Fortran subroutine for general quadratic programming”, Report AERE-R 6370, Harwell (1970)]. We conclude that the algorithm of Goldfarb and Idnani is very suitable in practice for convex quadratic programming calculations.
Keywords for this software
References in zbMATH (referenced in 27 articles )
Showing results 1 to 20 of 27.
Sorted by year (- Gill, Philip E.; Wong, Elizabeth: Methods for convex and general quadratic programming (2015)
- Exler, Oliver; Lehmann, Thomas; Schittkowski, Klaus: A comparative study of SQP-type algorithms for nonlinear and nonconvex mixed-integer optimization (2012)
- Kirches, Christian; Bock, Hans Georg; Schlöder, Johannes P.; Sager, Sebastian: A factorization with update procedures for a KKT matrix arising in direct optimal control (2011)
- Sapountzakis, E.J.; Kampitsis, A.E.: Nonlinear analysis of shear deformable beam-columns partially supported on tensionless three-parameter foundation (2011)
- Andretta, Marina; Birgin, Ernesto G.; Martínez, J.M.: Partial spectral projected gradient method with active-set strategy for linearly constrained optimization (2010)
- Vassiliou, E.E.; Demetriou, I.C.: A linearly distributed lag estimator with $r$-convex coefficients (2010)
- Karas, Elizabeth; Ribeiro, Ademir; Sagastizábal, Claudia; Solodov, Mikhail: A bundle-filter method for nonsmooth convex constrained optimization (2009)
- Schittkowski, Klaus: An active set strategy for solving optimization problems with up to 200,000,000 nonlinear constraints (2009)
- Zhang, Juliang; Shi, Yong; Zhang, Peng: Several multi-criteria programming methods for classification (2009)
- Übi, E.: A numerically stable least squares solution to the quadratic programming problem (2008)
- Bartlett, Roscoe A.; Biegler, Lorenz T.: QPSchur: A dual, active-set, Schur-complement method for large-scale and structured convex quadratic programming (2006)
- Demetriou, I.C.: L2CXCV: a Fortran 77 package for least squares convex/concave data smoothing (2006)
- Magazinović, G.: Two-point mid-range approximation enhanced recursive quadratic programming method (2005)
- Torney, David C.: Bayesian analysis of binary sequences (2005)
- Heath, W.P.; Wills, A.G.: Design of cross-directional controllers with optimal steady state performance (2004)
- Frangioni, Antonio: Solving semidefinite quadratic problems within nonsmooth optimization algorithms (1996)
- Demetriou, I.C.: Algorithm 742: L2CXFT: A Fortran subroutine for least-squares data fitting with nonnegative second divided differences (1995)
- Bartholomew-Biggs, M.C.; Nguyen, T.T.: Orthogonal and conjugate basis methods for solving equality constrained minimization problems (1993)
- Fletcher, R.: Resolving degeneracy in quadratic programming (1993)
- Burton, D.; Toint, Ph.L.: On an instance of the inverse shortest paths problem (1992)