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The relief indicator method for constrained global optimization

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  • Phan Thiên Thach
  • Hoàng Tuy

Abstract

We consider the problem of globally minimizing a continuous, not‐necessarily smooth function f(x) over a compact set S in Rn. To each real number α we associate a function φα(x), called the relief indicator, such that the function φαα(x) + ∥x∥2 is closed, convex, and a feasible point x is a global optimal solution if and only if 0 = min{φα(x): x ∈ Rn}, where α = f(x). Based on this global optimality criterion, an algorithm is then developed which reduces the problem to a sequence of linearly constrained concave quadratic separable programs. We discuss the practical use of these results when n (the number of variables) is small and also show how the method can be applied in the decomposition of certain nonconvex problems.

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  • Phan Thiên Thach & Hoàng Tuy, 1990. "The relief indicator method for constrained global optimization," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(4), pages 473-497, August.
    • Handle: RePEc:wly:navres:v:37:y:1990:i:4:p:473-497
    DOI: 10.1002/1520-6750(199008)37:43.0.CO;2-O
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    References listed on IDEAS

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    1. B. Kalantari & J. B. Rosen, 1987. "An Algorithm for Global Minimization of Linearly Constrained Concave Quadratic Functions," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 544-561, August.
    2. Reiner Horst, 1990. "Deterministic methods in constrained global optimization: Some recent advances and new fields of application," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(4), pages 433-471, August.
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