Index branch-and-bound algorithm for Lipschitz univariate global optimization with multiextremal constraints

In this paper, Lipschitz univariate constrained global optimization problem s where both the objective function and constraints can be multiextremal ar e considered. The constrained problem is reduced to a discontinuous unconst rained problem by the index scheme without introducing additional parameter s or variables. A Branch-and-Bound method that does not use derivatives for solving the reduced problem is proposed. The method either determines the infeasibility of the original problem or finds lower and upper bounds for t he global solution. Not all the constraints are evaluated during every iter ation of the algorithm, providing a significant acceleration of the search. Convergence conditions of the new method are established. Extensive numeri cal experiments are presented.