Abstract
This work concerns the global optimization of a continuous objective function f on a closed bounded domain S ⊂ R n . Neither f nor S are assumed to be convex, but the point of global minimum x* is assumed to be unique on S. We establish a representation formula for the point of global optimum, analogous to the Feynman-Kac representations of the solutions of boundary value problems. The representation suggests a simple numerical algorithm for the approximation of x*. An improvement of the simple algorithm is proposed by using a combination between the representation formula and stochastic perturbations of a descent algorithm. Numerical Examples are given and establish that the method is effective to calculate.
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de Cursi, J.E.S. (2004). Representation and numerical determination of the global optimizer of a continuous function on a bounded domain. In: Floudas, C.A., Pardalos, P. (eds) Frontiers in Global Optimization. Nonconvex Optimization and Its Applications, vol 74. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0251-3_28
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DOI: https://doi.org/10.1007/978-1-4613-0251-3_28
Publisher Name: Springer, Boston, MA
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