A derivative based algorithm for a particular class of mixed variables optimization problems

In this article, we consider a particular class of nonlinear mixed variable optimization problems where the structure and the number of variables of the problem depend on the values of some discrete variables. The peculiarity of this class is that, for fixed values of the integer variables, the corresponding continuous optimization problem contains no constraints and a large number of variables. For such a class of problems we propose two minimization algorithms and prove their global convergence properties.