PARABOLOID TRIANGULATION METHODS IN SOLVING MULTIEXTREMAL OPTIMIZATION PROBLEMS WITH CONSTRAINTS FOR A CLASS OF FUNCTIONS WITH LIPSCHITZ DIRECTIONAL DERIVATIVES
A new method is proposed to solve multiextremal problems with nonconvex constraints for a class of functions with Lipschitz directional derivatives. Only function values are measured. Adaptive triangulation of the search region with irregular simplexes is applied. Minorants of functions in simplexes are constructed as paraboloids. The method reduces the problem with constraints to a problem on a hyper interval with a configurable objective function. Convergence conditions for the reduction process have been obtained. Computational experiment results are presented.