Global Optimization Algorithm Using Local Lipschitz Constant Estimate - Gimbutas, Albertas (Jaunųjų mokslininkų darbai, 2016)
In this paper, we propose a new deterministic global optimization algorithm for black-box Lipschitz functions with an unknown Lipschitz constant. At the beginning of the proposed algorithm the feasible region is divided into simplices. At each iteration of algorithm the local Lipschitz constant estimate is found and the lowest possible function value over the simplex is estimated for each simplex; the most promising simplices are selected and divided. An inner optimization problem is solved to find the lowest possible function value estimate for each simplex. A sub-algorithm is proposed to solve the inner optimization problem. Experiments were performed with two- and three- dimensional optimization problems using 400 test functions generated with the GKLS generator. The results showed that complex problems can be solved with less function evaluations using the proposed algorithm than using other most popular alternatives.