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Value-Estimation Function Method for Constrained Global Optimization

Author

Listed:
  • X. L. Sun

    (Shanghai University)

  • D. Li

    (Chinese University of Hong Kong)

Abstract

A novel value-estimation function method for global optimization problems with inequality constraints is proposed in this paper. The value-estimation function formulation is an auxiliary unconstrained optimization problem with a univariate parameter that represents an estimated optimal value of the objective function of the original optimization problem. A solution is optimal to the original problem if and only if it is also optimal to the auxiliary unconstrained optimization with the parameter set at the optimal objective value of the original problem, which turns out to be the unique root of a basic value-estimation function. A logarithmic-exponential value-estimation function formulation is further developed to acquire computational tractability and efficiency. The optimal objective value of the original problem as well as the optimal solution are sought iteratively by applying either a generalized Newton method or a bisection method to the logarithmic-exponential value-estimation function formulation. The convergence properties of the solution algorithms guarantee the identification of an approximate optimal solution of the original problem, up to any predetermined degree of accuracy, within a finite number of iterations.

Suggested Citation

  • X. L. Sun & D. Li, 1999. "Value-Estimation Function Method for Constrained Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 385-409, August.
    • Handle: RePEc:spr:joptap:v:102:y:1999:i:2:d:10.1023_a:1021736608968
    DOI: 10.1023/A:1021736608968
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    Cited by:

    1. Xiaoling Sun & Duan Li, 2000. "Asymptotic Strong Duality for Bounded Integer Programming: A Logarithmic-Exponential Dual Formulation," Mathematics of Operations Research, INFORMS, vol. 25(4), pages 625-644, November.
    2. Duan Yaqiong & Lian Shujun, 2016. "Smoothing Approximation to the Square-Root Exact Penalty Function," Journal of Systems Science and Information, De Gruyter, vol. 4(1), pages 87-96, February.

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