Test Problems for Lipschitz Univariate Global Optimization with Multiextremal Constraints

Abstract. In this paper, Lipschitz univariate constrained global optimization problems where both the objective function and constraints can be multiextremal are considered. Two sets of test problems are introduced, in the first one both the objective function and constraints are differentiable functions and in the second one they are non-differentiable. Each series of tests contains 3 problems with one constraint, 4 problems with 2 constraints, 3 problems with 3 constraints, and one infeasible problem with 2 constraints. All the problems are shown in Figures. Lipschitz constants and global solutions are given. For each problem it is indicated whether the optimum is located on the boundary or inside a feasible subregion and the number of disjoint feasible subregions is given. Results of numerical experiments executed with the introduced test problems using Pijavskii’s method combined with a non-differentiable penalty function are presented.