An interior point algorithm for convex quadratic programming with strict equilibrium constraints

Rachid Benouahboun; Abdelatif Mansouri

RAIRO - Operations Research (2010)

  • Volume: 39, Issue: 1, page 13-33
  • ISSN: 0399-0559

Abstract

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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 ( 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.

How to cite

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Benouahboun, Rachid, and Mansouri, Abdelatif. "An interior point algorithm for convex quadratic programming with strict equilibrium constraints." RAIRO - Operations Research 39.1 (2010): 13-33. <http://eudml.org/doc/105320>.

@article{Benouahboun2010,
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. },
author = {Benouahboun, Rachid, Mansouri, Abdelatif},
journal = {RAIRO - Operations Research},
keywords = {Convex quadratic programming with a strict equilibrium constraints; interior point algorithm; Newton's method.; Convex quadratic programming with a strict equilibrium constraints; Newton's method},
language = {eng},
month = {3},
number = {1},
pages = {13-33},
publisher = {EDP Sciences},
title = {An interior point algorithm for convex quadratic programming with strict equilibrium constraints},
url = {http://eudml.org/doc/105320},
volume = {39},
year = {2010},
}

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
DA - 2010/3//
PB - EDP Sciences
VL - 39
IS - 1
SP - 13
EP - 33
AB - 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.
LA - eng
KW - Convex quadratic programming with a strict equilibrium constraints; interior point algorithm; Newton's method.; Convex quadratic programming with a strict equilibrium constraints; Newton's method
UR - http://eudml.org/doc/105320
ER -

References

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  1. H.P. Benson, Optimization over the efficient set. J. Math. Anal. Appl.98 (1984) 562–580.  Zbl0534.90077
  2. H.P. Benson, An algorithm for optimizing over the weakly-efficient set. European J. Oper. Res.25 (1986) 192–199.  Zbl0594.90082
  3. Y. Chen and M. Florian, O-D demand adjustment problem with cojestion: Part I. Model analysis and optimality conditions. Publication CRT-94-56.  
  4. C. Cinquini and R. Contro, Optimal design of beams discretized by elastic plastic finite element. Comput. Structures20 (1985) 475–585.  Zbl0581.73103
  5. A.V. Fiacco and G.P. McCormick, Nonlinear Programming: Sequential Unconstrained Minmization Techniques. John Wiley, New York (1968).  Zbl0193.18805
  6. D. Gale, The theory of Linear Economic. McGraw-Hill Book Company, New York (1960).  
  7. C. Gonzaga, Path-following methods for linear programming. SIAM Rev.34 (1992) 167–274.  Zbl0763.90063
  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.  Zbl0717.90055
  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).  Zbl0952.49034
  10. G. Maier, A quadratic programming approach for certain classes of nonlinear structural problems. Meccanica3 (1968) 121–130.  Zbl0165.28502
  11. D.C. Monteiro and I. Adler, Interior path following primal-dual algorithms. Part I: Linear programming. Math. Prog.44 (1989) 27–41.  Zbl0676.90038
  12. Z.Q. Luo, J.S Pang and D. Ralph, Mathematical Programs with Equilibrium Constraints. Cambridge University Press (1996).  Zbl1139.90003

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