An Augmented Lagrangian-Based Method Using Primitive Directions for Mixed-Integer Nonlinear Problems

Abstract In this paper, we consider mixed-integer nonlinear constrained optimization problems. Specifically, we assume that the integrality constraints are non-relaxable, that is, the functions appearing in the problem cannot be computed when the integrality constraints are violated. To solve this class of problems, we propose an augmented Lagrangian-type algorithm which is able to handle integer variables by means of primitive directions. A theoretical analysis of the convergence properties of the proposed algorithm is carried out. Finally, some numerical experimentation is reported.