Convergence of derivative-free nonmonotone Direct Search Methods for unconstrained and box-constrained mixed-integer optimization

Abstract This paper presents a class of nonmonotone Direct Search Methods that converge to stationary points unconstrained and boxed constrained mixed-integer optimization problems. A new concept is introduced: the quasi-descent direction. point x on set search directions if there exists no feasible qdd set. The method does not require computation derivatives nor explicit manipulation asymptotically dense matrices. Preliminary numerical experiments carried out small medium problems are encouraging.