The paper continues the study of the previously proposed index method for solving constrained global optimization problems with the objective function and left-hand sides of the constraints satisfying Lipschitz condition. One-dimensional problems with ε-reserved solutions are under consideration. The upper bounds of the reserves values, which maintain the convergence of the method to the exact constrained optimizer, are estimated. By constructing estimates of the trials density in the subintervals of the search domain, it is shown that an increase in the reserve values used in the algorithm accelerates the convergence of the method. A new modification of the algorithm using adaptive estimates of reserves is proposed. The results of numerical experiments are given.

global optimization; multiextremal functions; nonconvex constraints; ε-reserved solutions

Mathematical problems and theory of numerical methods