Combined approach to solve linear complementarity problem

Authors

  • Kebbiche Zakia Department of mathematics, Faculty of Sciences, University of Ferhat Abbas, Sétif1, Algeria
  • Roumili Hayet Department of mathematics, Faculty of Sciences, University of Ferhat Abbas, Sétif1, Algeria

DOI:

https://doi.org/10.33993/jnaat452-1088

Keywords:

linear complementarity problem, Lemke algorithm, quadratic convex program, linear program, pivot
Abstract views: 247

Abstract

In this paper, we present a new approach in order to solve the linear complementary problem noted (LCP). We have combined the ideas of Lemke's method and its variants taking advantage of the benefits of each approach in order to improve the convergence of these algorithms.
Numerical simulations and comparative results of the new approach are provided.
Since the quadratic convex program and linear program can be written as (LCP), so it can be resolved thanks to our new approach.

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References

M. Bazarra, H.D. Sherali and C.M. Shetty, Nonlinear Programming: Theory and Algorithms, Second edition, Wiley, 1993, http://dx.doi.org/10.1002/0471787779 DOI: https://doi.org/10.1002/0471787779

I. Ben Gharbia, Resolution de probemes de complementarite: Applications a un ecoulement diphasique dans un milieu poreux, Tese de Doctorat, Universite Paris-Dauphine , 2012.

R.W. Cottle, J.S. Pang and R.E. Stone, The Linear Complementarity Problem, Academic Press, Inc., New York, 1992, http://dx.doi.org/10.1137/1.9780898719000 DOI: https://doi.org/10.1137/1.9780898719000

Dipti Dubey, J.M. Neogy, On hiden Z-matrices and the linear complementarity problem , Linear Algebra and its Applications, 496 (2016) no. 1, pp. 81-100, 2016, http://dx.doi.org/10.1016/j.laa.2016.01.045 DOI: https://doi.org/10.1016/j.laa.2016.01.045

M. Garcia-Esnaola, S.K. Pena, Error bounds for the linear complementarity problem with a Σ-SDD matrix, Linear Algebra and its Applications, 413 (2013) no. 3, pp. 1339-1346, DOI: https://doi.org/10.1016/j.laa.2012.09.018

C.E. Lemke, On complementary pivot theory, In Mathematic of the Decision Sciences, American Mathematical Society, pp. 95-114, 1968.

K.G. Murty, Linear Complementary, Linear and Nonlinear Programming, Helder Mann Verlag, 1988.

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Published

2016-12-10

How to Cite

Zakia, K., & Hayet, R. (2016). Combined approach to solve linear complementarity problem. J. Numer. Anal. Approx. Theory, 45(2), 163–176. https://doi.org/10.33993/jnaat452-1088

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