The relief indicator method for constrained global optimization

Phan Thiên Thach and Hoàng Tuy

Naval Research Logistics (NRL), 1990, vol. 37, issue 4, 473-497

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.

Date: 1990
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https://doi.org/10.1002/1520-6750(199008)37:43.0.CO;2-O

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Persistent link: https://EconPapers.repec.org/RePEc:wly:navres:v:37:y:1990:i:4:p:473-497

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