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

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 stat...

[1]  P. Gill,et al.  Conjugate-Gradient Methods for Large-Scale Nonlinear Optimization. , 1979 .

[2]  L. Grippo,et al.  Exact penalty functions in constrained optimization , 1989 .

[3]  Francisco Facchinei,et al.  An RQP algorithm using a differentiable exact penalty function for inequality constrained problems , 1992, Math. Program..

[4]  Jorge Nocedal,et al.  On the limited memory BFGS method for large scale optimization , 1989, Math. Program..

[5]  L. Grippo,et al.  A new augmented Lagrangian function for inequality constraints in nonlinear programming problems , 1982 .

[6]  Anthony V. Fiacco,et al.  Nonlinear programming;: Sequential unconstrained minimization techniques , 1968 .

[7]  L. Grippo,et al.  A differentiable exact penalty function for bound constrained quadratic programming problems , 1991 .

[8]  Stephen G. Nash,et al.  Block truncated-Newton methods for parallel optimization , 1989, Math. Program..

[9]  S. Lucidi,et al.  Recursive quadratic programming algorithm that uses an exact augmented Lagrangian function , 1990 .

[10]  Ya-Xiang Yuan,et al.  A recursive quadratic programming algorithm that uses differentiable exact penalty functions , 1986, Math. Program..

[11]  L. Grippo,et al.  A New Class of Augmented Lagrangians in Nonlinear Programming , 1979 .

[12]  S. Nash.  Preconditioning of Truncated-Newton Methods , 1985 .

[13]  S. Lucidi.  New results on a class of exact augmented Lagrangians , 1988 .

[14]  L. Grippo,et al.  An exact penalty function method with global convergence properties for nonlinear programming problems , 1986, Math. Program..