A Deterministic Global Optimization Method Based on Legendre-Fenchel Transform

摘要

This paper introduces a deterministic global continuous optimization method.Given some properties of the criterion function-the first and second order derivatives satisfy Lipschitz conditions or the criterion function is analytic-,it takes full advantage of some theoretical results related to the local convergence analysis of the Gauss-Newton method to calculate points,which may be global minima.This method is original in two ways.First,using the Gauss-Newton method,we try to find least squares solutions to an overdetermined system of global optimality conditions.Second,instead of solving the initial formulation,we apply a uniform scaling to the criterion function and obtain an equivalent problem,where the local convergence of the Gauss-Newton method is improved.The modified overdetermined system is solved from several initial points belonging to a simplicial research domain.This simplicial domain is subdivided recursively into smaller simplices until each of the covering simplices either contains no global minimum(exclusion),or contains one and only one global minimum(inclusion)