Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-23T13:02:17.203Z Has data issue: false hasContentIssue false
  • English
  • Français

An interior point algorithm for convex quadratic programming withstrict equilibrium constraints

Published online by Cambridge University Press:  15 July 2005

Rachid Benouahboun  and
Abdelatif Mansouri
Rachid Benouahboun
Affiliation:
Département de Mathématiques, Faculté des Sciences Semlalia, Marrakech, Maroc; mansouri@ucam.ac.ma
Abdelatif Mansouri
Affiliation:
Département de Mathématiques, Faculté des Sciences Semlalia, Marrakech, Maroc; mansouri@ucam.ac.ma
Get access

Abstract

We describe an interior point algorithm for convex quadratic problem with a strict complementarity constraints. We show that under some assumptions the approach requires a total of $O(\sqrt{n}L)$ number of iterations, where L is the input size of the problem. The algorithm generates a sequence of problems, each of which is approximately solved by Newton's method.

Keywords

Convex quadratic programming with a strict equilibrium constraintsinterior point algorithmNewton's method.
Type
Research Article
Information
RAIRO - Operations Research , Volume 39 , Issue 1 , January 2005 , pp. 13 - 33
Copyright
© EDP Sciences, 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Benson, H.P., Optimization over the efficient set. J. Math. Anal. Appl. 98 (1984) 562–580. CrossRef
Benson, H.P., An algorithm for optimizing over the weakly-efficient set. European J. Oper. Res. 25 (1986) 192–199. CrossRef
Y. Chen and M. Florian, O-D demand adjustment problem with cojestion: Part I. Model analysis and optimality conditions. Publication CRT-94-56.
Cinquini, C. and Contro, R., Optimal design of beams discretized by elastic plastic finite element. Comput. Structures 20 (1985) 475–585. CrossRef
A.V. Fiacco and G.P. McCormick, Nonlinear Programming: Sequential Unconstrained Minmization Techniques. John Wiley, New York (1968).
D. Gale, The theory of Linear Economic. McGraw-Hill Book Company, New York (1960).
Gonzaga, C., Path-following methods for linear programming. SIAM Rev. 34 (1992) 167–274. CrossRef
D. Goldfarb and S. Liu, An $O(n^{3}L)$ primal interior point algorithm for convex quadratic programming. Math. Prog. 49 (1990/91) 325–340.
M. Kočvara and J.V. Outrata, On the solution of optimum design problems with variational inequalities, in Recent Advances in Nonsmooth Optimization, edited by D.Z. Du, L. Qi and R. Womersly, World Sciences (November 1995).
Maier, G., A quadratic programming approach for certain classes of nonlinear structural problems. Meccanica 3 (1968) 121–130. CrossRef
Monteiro, D.C. and Adler, I., Interior path following primal-dual algorithms. Part I: Linear programming. Math. Prog. 44 (1989) 27–41. CrossRef
Z.Q. Luo, J.S Pang and D. Ralph, Mathematical Programs with Equilibrium Constraints. Cambridge University Press (1996).