Constraint Logic Programming for Non Convex NLP and MINLP Problems

Abstract

This paper presents an algorithm to solve non-convex NLP and MINLP problems using CLP. In the proposed technique, the continuous variables are relaxed to take only integer values contained in the real domain of the variable. The merits of the CLP algorithm, viz powerful CP strategies are proposed to be exploited to get integer solutions to the relaxations. A lower bound to the objective function is obtained if the relaxed problem is feasible. This information is used in the successive stages wherein the continuous variables are corrected from their integer variable representation to obtain real solutions with desired accuracy. The proposed technique has been successfully demonstrated on two MILP, two non convex NLP and two non convex MINLP problems. The problems were also solved by traditional techniques and the superiority of the proposed method has been demonstrated.