Abstract
It is known that the problem of minimizing a convex functionf(x) over a compact subsetX of ℝn can be expressed as minimizing max{g(x, y)|y ∈X}, whereg is a support function forf[f(x) ≥g(x, y), for ally ∈X andf(x)=g(x, x)]. Standard outer-approximation theory can then be employed to obtain outer-approximation algorithms with procedures for dropping previous cuts. It is shown here how this methodology can be extended to nonconvex nondifferentiable functions.
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This research was supported by the Science and Engineering Research Council, UK, and by the National Science Foundation under Grant No. ECS-79-13148.
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Mayne, D.Q., Polak, E. Outer approximation algorithm for nondifferentiable optimization problems. J Optim Theory Appl 42, 19–30 (1984). https://doi.org/10.1007/BF00934131
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DOI: https://doi.org/10.1007/BF00934131