Stochastic global optimization using tangent minorants for Lipschitz functions

[摘要] This paper deals with global stochastic optimization where the decision variable belongs to a compact subset X of R. The objective function is the mathematical expectation of a partial bivariate Lipschitz function f (x, Theta) depending on a decision variable x and a random variable Theta, whose probability distribution depends on x. In the first part of the present paper, we propose a branch and bound algorithm based on tangent minorants that provides a global minimum. In the second part, we consider the case where the function f is discontinuous. We show the manner we correct that discontinuity without modifying the global minimum of E (x, Theta)). We also illustrate how to extend this framework to multidimensional stochastic optimization problems by using the Alienor method. Then we validate the proposed method by applying it to some test functions and compare it to known algorithms. (C) 2019 Elsevier B.V. All rights reserved.

[发布日期] 2020-08-01

[效力级别]  Proceedings Paper

[关键词] Global optimization;Branch and bounds;Lipschitz functions;Lower semi-continuous functions;Underestimators;Tangent minorants