Diagonal generalizaton of the direct method for problems with constraints

The DIRECT method solves Lipschitz global optimization problems on a hyperinterval with an unlimited range of Lipschitz constants. We propose an extension of the DIRECT method principles to problems with multiextremal constraints is proposed when two evaluations of functions at the ends of the chosen main diagonals are used at once. We present computational illustrations, including the solution of a problem with discontinuities. We also perform convergence analysis.