An interior point algorithm for convex quadratic programming with strict equilibrium constraints
RAIRO - Operations Research - Recherche Opérationnelle, Tome 39 (2005) no. 1, pp. 13-33.

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(nL) 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.

DOI : 10.1051/ro:2005002
Mots clés : convex quadratic programming with a strict equilibrium constraints, interior point algorithm, Newton's method
@article{RO_2005__39_1_13_0,
     author = {Benouahboun, Rachid and Mansouri, Abdelatif},
     title = {An interior point algorithm for convex quadratic programming with strict equilibrium constraints},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {13--33},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {1},
     year = {2005},
     doi = {10.1051/ro:2005002},
     mrnumber = {2166343},
     zbl = {1102.90041},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro:2005002/}
}
TY  - JOUR
AU  - Benouahboun, Rachid
AU  - Mansouri, Abdelatif
TI  - An interior point algorithm for convex quadratic programming with strict equilibrium constraints
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2005
SP  - 13
EP  - 33
VL  - 39
IS  - 1
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ro:2005002/
DO  - 10.1051/ro:2005002
LA  - en
ID  - RO_2005__39_1_13_0
ER  - 
%0 Journal Article
%A Benouahboun, Rachid
%A Mansouri, Abdelatif
%T An interior point algorithm for convex quadratic programming with strict equilibrium constraints
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2005
%P 13-33
%V 39
%N 1
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ro:2005002/
%R 10.1051/ro:2005002
%G en
%F RO_2005__39_1_13_0
Benouahboun, Rachid; Mansouri, Abdelatif. An interior point algorithm for convex quadratic programming with strict equilibrium constraints. RAIRO - Operations Research - Recherche Opérationnelle, Tome 39 (2005) no. 1, pp. 13-33. doi : 10.1051/ro:2005002. http://www.numdam.org/articles/10.1051/ro:2005002/

[1] H.P. Benson, Optimization over the efficient set. J. Math. Anal. Appl. 98 (1984) 562-580. | Zbl

[2] H.P. Benson, An algorithm for optimizing over the weakly-efficient set. European J. Oper. Res. 25 (1986) 192-199. | Zbl

[3] Y. Chen and M. Florian, O-D demand adjustment problem with cojestion: Part I. Model analysis and optimality conditions. Publication CRT-94-56. | Zbl

[4] C. Cinquini and R. Contro, Optimal design of beams discretized by elastic plastic finite element. Comput. Structures 20 (1985) 475-585. | Zbl

[5] A.V. Fiacco and G.P. Mccormick, Nonlinear Programming: Sequential Unconstrained Minmization Techniques. John Wiley, New York (1968). | MR | Zbl

[6] D. Gale, The theory of Linear Economic. McGraw-Hill Book Company, New York (1960). | MR

[7] C. Gonzaga, Path-following methods for linear programming. SIAM Rev. 34 (1992) 167-274. | Zbl

[8] 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. | Zbl

[9] 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). | MR | Zbl

[10] G. Maier, A quadratic programming approach for certain classes of nonlinear structural problems. Meccanica 3 (1968) 121-130. | Zbl

[11] D.C. Monteiro and I. Adler, Interior path following primal-dual algorithms. Part I: Linear programming. Math. Prog. 44 (1989) 27-41. | Zbl

[12] Z.Q. Luo, J.S Pang and D. Ralph, Mathematical Programs with Equilibrium Constraints. Cambridge University Press (1996). | MR | Zbl

Cité par Sources :