An exact penalty approach for solving a class of minimization problems with Boolean variables

An exact penalty approach for solving minimization problems with a concave objective function, linear constraints and Boolean variables is proposed. The penalty problems have continuous variables. An estimation of the penalty parameter which guarantees the exactness can be calculated on the base of an auxiliary problem. The results are applied to problems with an arbitrary quadratic objective function, linear constraints and Boolean variables. This leads to a modified Lagrangian approach for the latter problems. In the general case, the penalty approach is compared with a direct application of results of global optimization to a modification of the initial problem.