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Solving nearly-separable quadratic optimization problems as nonsmooth equations

Author

Listed:
  • Frank E. Curtis

    (Lehigh University)

  • Arvind U. Raghunathan

    (Mitsubishi Electric Research Laboratories)

Abstract

An algorithm for solving nearly-separable quadratic optimization problems (QPs) is presented. The approach is based on applying a semismooth Newton method to solve the implicit complementarity problem arising as the first-order stationarity conditions of such a QP. An important feature of the approach is that, as in dual decomposition methods, separability of the dual function of the QP can be exploited in the search direction computation. Global convergence of the method is promoted by enforcing decrease in component(s) of a Fischer–Burmeister formulation of the complementarity conditions, either via a merit function or through a filter mechanism. The results of numerical experiments when solving convex and nonconvex instances are provided to illustrate the efficacy of the method.

Suggested Citation

  • Frank E. Curtis & Arvind U. Raghunathan, 2017. "Solving nearly-separable quadratic optimization problems as nonsmooth equations," Computational Optimization and Applications, Springer, vol. 67(2), pages 317-360, June.
    • Handle: RePEc:spr:coopap:v:67:y:2017:i:2:d:10.1007_s10589-017-9895-8
    DOI: 10.1007/s10589-017-9895-8
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    References listed on IDEAS

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    1. Jacek Gondzio & Andreas Grothey, 2007. "Parallel interior-point solver for structured quadratic programs: Application to financial planning problems," Annals of Operations Research, Springer, vol. 152(1), pages 319-339, July.
    2. Todd S. Munson & Francisco Facchinei & Michael C. Ferris & Andreas Fischer & Christian Kanzow, 2001. "The Semismooth Algorithm for Large Scale Complementarity Problems," INFORMS Journal on Computing, INFORMS, vol. 13(4), pages 294-311, November.
    3. Quoc Tran Dinh & Ion Necoara & Moritz Diehl, 2014. "Path-following gradient-based decomposition algorithms for separable convex optimization," Journal of Global Optimization, Springer, vol. 59(1), pages 59-80, May.
    4. NESTEROV, Yu., 2005. "Excessive gap technique in nonsmooth convex minimization," LIDAM Reprints CORE 1818, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Quoc Tran Dinh & Carlo Savorgnan & Moritz Diehl, 2013. "Combining Lagrangian decomposition and excessive gap smoothing technique for solving large-scale separable convex optimization problems," Computational Optimization and Applications, Springer, vol. 55(1), pages 75-111, May.
    6. NESTEROV, Yu., 2005. "Smooth minimization of non-smooth functions," LIDAM Reprints CORE 1819, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Stuart M. Harwood, 2021. "Analysis of the Alternating Direction Method of Multipliers for Nonconvex Problems," SN Operations Research Forum, Springer, vol. 2(1), pages 1-29, March.

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