An exact penalty-lagrangian approach for a class of constrained optimization problems with bounded variables

Abstract

In this paper we consider a class of equality constrained optimization problems with box constraints on a part of its variables

The study of non linear programming problems with such a structure is justified by the existence of practical problems in many fields as, for example, optimal control or economic modelling. Typically, the dimension of these problems are very large and, in such situation, the classical methods to solve NLP problems may have serious drawbacks. In this paper we define a new continuosly differentiable exact penalty function which transforms the original constrained problem into an unconstrained one and it is well suited to tackle large scale problems. In particular this new function is based on a mixed exact penalty-Lagrangian approach and this allows us to take full advantage of the particular structure of the considered class of problems. We show that there is a one to one correspondence between Kuhn-Tucker point (local and global minimum points) of the constrained problem and stationary point (local and global minimum points) of the merit function. Thus, the unconstrained minimization of the exact penalty-Lagrangian function yields the solution of the original constrained problem

Keywords:

• Exact penalty Function
• Exact Augmented Lagrangian Function
• Non Linear Programming
• Constrained Optimization