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

An exact penalty-lagrangian approach for a class of constrained optimization problems with bounded variables / DI PILLO, Gianni; Lucidi, Stefano; Palagi, Laura. - In: OPTIMIZATION. - ISSN 0233-1934. - STAMPA. - 28:2(1993), pp. 129-148. [10.1080/02331939308843909]

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

DI PILLO, Gianni;LUCIDI, Stefano;PALAGI, Laura
1993

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
exact augmented lagrangian function; exact penalty function; non linear programming
01 Pubblicazione su rivista::01a Articolo in rivista
An exact penalty-lagrangian approach for a class of constrained optimization problems with bounded variables / DI PILLO, Gianni; Lucidi, Stefano; Palagi, Laura. - In: OPTIMIZATION. - ISSN 0233-1934. - STAMPA. - 28:2(1993), pp. 129-148. [10.1080/02331939308843909]
File allegati a questo prodotto
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/243372
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 9
  • ???jsp.display-item.citation.isi??? ND
social impact