Mesh adaptive direct search algorithms for mixed variable optimization

In previous work, the generalized pattern search (GPS) algorithm for linearly constrained (continuous) optimization was extended to mixed variable problems, in which some of the variables may be categorical. In another paper, the mesh adaptive direct search (MADS) algorithm was introduced as a generalization of GPS for problems with general nonlinear constrained. The convergence analyses of these methods rely on the Clarke calculus for nonsmooth functions. In the present paper, we generalize both of these approaches by proposing an algorithm for problems with both mixed variables and general nonlinear constraints, called mixed variable-MADS (MV-MADS). A new convergence analysis is presented which generalizes the existing GPS and MADS theory.