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Decomposition in derivative-free optimization

Author

Listed:
  • Kaiwen Ma

    (Carnegie Mellon University)

  • Nikolaos V. Sahinidis

    (Georgia Institute of Technology)

  • Sreekanth Rajagopalan

    (The Dow Chemical Company)

  • Satyajith Amaran

    (The Dow Chemical Company)

  • Scott J Bury

    (The Dow Chemical Company)

Abstract

This paper proposes a novel decomposition framework for derivative-free optimization (DFO) algorithms. Our framework significantly extends the scope of current DFO solvers to larger-scale problems. We show that the proposed framework closely relates to the superiorization methodology that is traditionally used for improving the efficiency of feasibility-seeking algorithms for constrained optimization problems in a derivative-based setting. We analyze the convergence behavior of the framework in the context of global search algorithms. A practical implementation is developed and exemplified with the global model-based solver Stable Noisy Optimization by Branch and Fit (SNOBFIT) [36]. To investigate the decomposition framework’s performance, we conduct extensive computational studies on a collection of over 300 test problems of varying dimensions and complexity. We observe significant improvements in the quality of solutions for a large fraction of the test problems. Regardless of problem convexity and smoothness, decomposition leads to over 50% improvement in the objective function after 2500 function evaluations for over 90% of our test problems with more than 75 variables.

Suggested Citation

  • Kaiwen Ma & Nikolaos V. Sahinidis & Sreekanth Rajagopalan & Satyajith Amaran & Scott J Bury, 2021. "Decomposition in derivative-free optimization," Journal of Global Optimization, Springer, vol. 81(2), pages 269-292, October.
    • Handle: RePEc:spr:jglopt:v:81:y:2021:i:2:d:10.1007_s10898-021-01051-w
    DOI: 10.1007/s10898-021-01051-w
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    References listed on IDEAS

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    1. NESTEROV, Yurii, 2013. "Gradient methods for minimizing composite functions," LIDAM Reprints CORE 2510, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    4. Yair Censor & Alexander J. Zaslavski, 2015. "Strict Fejér Monotonicity by Superiorization of Feasibility-Seeking Projection Methods," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 172-187, April.
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