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Solution of Monotone Complementarity and General Convex Programming Problems Using a Modified Potential Reduction Interior Point Method

Author

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  • Kuo-Ling Huang

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

  • Sanjay Mehrotra

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

Abstract

We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition (SLC) is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear and polynomial time convergence properties, while achieving practical performance. It either successfully solves the problem, or concludes that the SLC is not satisfied. When compared with the mature software package MOSEK (barrier solver version 6.0.0.106), iOptimize solves convex quadratic programming problems, convex quadratically constrained quadratic programming problems, and general convex programming problems in fewer iterations. Moreover, several problems for which MOSEK fails are solved to optimality. We also find that iOptimize detects infeasibility more reliably than the general nonlinear solvers Ipopt (version 3.9.2) and Knitro (version 8.0).

Suggested Citation

  • Kuo-Ling Huang & Sanjay Mehrotra, 2017. "Solution of Monotone Complementarity and General Convex Programming Problems Using a Modified Potential Reduction Interior Point Method," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 36-53, February.
    • Handle: RePEc:inm:orijoc:v:29:y:2017:i:1:p:36-53
    DOI: 10.1287/ijoc.2016.0715
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    References listed on IDEAS

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    1. Yinyu Ye & Michael J. Todd & Shinji Mizuno, 1994. "An O(√nL)-Iteration Homogeneous and Self-Dual Linear Programming Algorithm," Mathematics of Operations Research, INFORMS, vol. 19(1), pages 53-67, February.
    2. S. Cafieri & M. D’Apuzzo & V. Simone & D. Serafino & G. Toraldo, 2007. "Convergence Analysis of an Inexact Potential Reduction Method for Convex Quadratic Programming," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 355-366, December.
    3. Yu. E. Nesterov & M. J. Todd, 1997. "Self-Scaled Barriers and Interior-Point Methods for Convex Programming," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 1-42, February.
    4. Michael J. Todd & Yinyu Ye, 1990. "A Centered Projective Algorithm for Linear Programming," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 508-529, August.
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    Cited by:

    1. Cosmin G. Petra & Florian A. Potra, 2019. "A homogeneous model for monotone mixed horizontal linear complementarity problems," Computational Optimization and Applications, Springer, vol. 72(1), pages 241-267, January.
    2. Chuangyin Dang & P. Jean-Jacques Herings & Peixuan Li, 2022. "An Interior-Point Differentiable Path-Following Method to Compute Stationary Equilibria in Stochastic Games," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1403-1418, May.

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