{"title":"A Dual Method for Solving General Convex Quadratic Programs","authors":"Belkacem Brahmi, Mohand Ouamer Bibi","volume":34,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":825,"pagesEnd":830,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/8966","abstract":"
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.<\/p>\r\n","references":"[1] R. Gabasov, F. M. Kirillova and V. M. Raketsky. On methods for solving\r\nthe general problem of convex quadratic programming. Soviet. Math.\r\nDokl. 23 (1981) 653-657.\r\n[2] R. Gabasov, F. M. Kirillova, V. M. Raketsky and O.I. Kostyukova.\r\nConstructive Methods of Optimization, Volume 4: Convex Problems.\r\nUniversity Press, Minsk (1987).\r\n[3] E. A. Kostina and O. I. Kostyukova. An algorithm for solving quadratic\r\nprogramming problems with linear equality and inequality constraints. Computational Mathematics and Mathematical Physics, 41(7) (2001) 960-973.\r\n[4] E. A. Kostina and O. I. Kostyukova. A primal-dual active-set method for\r\nconvex quadratic programming. Preprints of the University of Karlsruhe,\r\nGermany (2003).\r\n[5] B. Brahmi and M. O. Bibi. Dual support method for solving convex\r\nquadratic programs. To appear in Optimization (2009).\r\n[6] R. Fletcher. Practical Methods of Optimization. J. Wiley and Sons,\r\nChichester, England, second edition (1987).\r\n[7] P. E. Gill, W. Murray, and M. H. Wright. Practical Optimization.\r\nAcademic Press Inc, London ( 1981).\r\n[8] Y. Nesterov and A. Nemirovskii. Interior-Point Polynomial Algorithms\r\nin Convex Programming. SIAM Studies in Applied Mathematics: Vol\r\n13, Philadelphia (1994).\r\n[9] J. Nocedal and S. J. Wright. Numerical Optimization. Springer-Verlag,\r\nNew York, second edition (2006).\r\n[10] N. L. Boland. A dual-active-set algorithm for positive semi-definite\r\nquadratic programming. Mathematical Programming, 78(1)(1997)1-27.\r\n[11] D. Goldfarb and A. U. Idnani. A numerically stable dual method for\r\nsolving strictly convex quadratic problems. Mathematical Programming,\r\n27 (1983) 1-33.\r\n[12] C. Van de Panne and A. Whinston. The simplex and dual method for\r\nquadratic programming. Operational Research Quarterly Journal, 15\r\n(1964) 355-388.\r\n[13] R. A. Bartlett and L. T. Biegler. QPSchur: A dual, active-set, Schurcomplement\r\nmethod for large-scale and structured convex quadratic\r\nprogramming. Optimization and Engineering, 7 (2006) 5-32.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 34, 2009"}