A Dual Method for Solving General Convex Quadratic Programs
In this paper, we present a new method for solving quadratic programming problems, not strictly convex. Constraints of the problem are linear equalities and inequalities, with bounded variables. The suggested method combines the active-set strategies and support methods. The algorithm of the method and numerical experiments are presented, while comparing our approach with the active set method on randomly generated problems.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1071882Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1527
 R. Gabasov, F. M. Kirillova and V. M. Raketsky. On methods for solving the general problem of convex quadratic programming. Soviet. Math. Dokl. 23 (1981) 653-657.
 R. Gabasov, F. M. Kirillova, V. M. Raketsky and O.I. Kostyukova. Constructive Methods of Optimization, Volume 4: Convex Problems. University Press, Minsk (1987).
 E. A. Kostina and O. I. Kostyukova. An algorithm for solving quadratic programming problems with linear equality and inequality constraints. Computational Mathematics and Mathematical Physics, 41(7) (2001) 960-973.
 E. A. Kostina and O. I. Kostyukova. A primal-dual active-set method for convex quadratic programming. Preprints of the University of Karlsruhe, Germany (2003).
 B. Brahmi and M. O. Bibi. Dual support method for solving convex quadratic programs. To appear in Optimization (2009).
 R. Fletcher. Practical Methods of Optimization. J. Wiley and Sons, Chichester, England, second edition (1987).
 P. E. Gill, W. Murray, and M. H. Wright. Practical Optimization. Academic Press Inc, London ( 1981).
 Y. Nesterov and A. Nemirovskii. Interior-Point Polynomial Algorithms in Convex Programming. SIAM Studies in Applied Mathematics: Vol 13, Philadelphia (1994).
 J. Nocedal and S. J. Wright. Numerical Optimization. Springer-Verlag, New York, second edition (2006).
 N. L. Boland. A dual-active-set algorithm for positive semi-definite quadratic programming. Mathematical Programming, 78(1)(1997)1-27.
 D. Goldfarb and A. U. Idnani. A numerically stable dual method for solving strictly convex quadratic problems. Mathematical Programming, 27 (1983) 1-33.
 C. Van de Panne and A. Whinston. The simplex and dual method for quadratic programming. Operational Research Quarterly Journal, 15 (1964) 355-388.
 R. A. Bartlett and L. T. Biegler. QPSchur: A dual, active-set, Schurcomplement method for large-scale and structured convex quadratic programming. Optimization and Engineering, 7 (2006) 5-32.