Nonmonotone algorithms for pattern search methods

This work deals with the solution of ill-conditioned unconstrained minimization problems by means of pattern search methods. To this end, the Usual requirement of monotonic reduction of the objective function is relaxed and nonmonotone pattern search methods are proposed, which maintain the convergence properties of their monotone counterparts. Numerical experimentation on several well-known ill-conditioned functions is reported. The results highlight a class of pattern search methods which benefit very much by the introduction of nonmonotone strategies.