Constrained optimization with integer and continuous variables using inexact restoration and projected gradients

Inexact restoration (IR) is a well established technique for continuous minimization problems with constraints that can be applied to constrained optimization problems with specific structures. When some variables are restricted to be integer, an IR strategy seems to be appropriate. The IR strategy employs a restoration procedure in which one solves a standard nonlinear programming problem and an optimization procedure in which the constraints are linearized and techniques for mixed-integer (linear or quadratic) programming can be employed.