This paper is concerned with the problem of strong duality between an infinite dimensional convex optimization problem with cone and equality constraints and its Lagrange dual. A necessary and sufficient condition and sufficient conditions, really new, in order that the strong duality holds true are given. As an application, the existence of the Lagrange multiplier associated with the obstacle problem and to an elastic–plastic torsion problem, more general than the ones Previously considered, is stated together with a characterization of the elastic–plastic torsion problem. This application is the main result of the paper. It is worth remarking that the usual conditions based on the interior, on the core, on the intrinsic core or on the strong quasi-relative interior cannot be used because they require the nonemptiness of the interior (and of the above mentioned generalized interior concepts) of the ordering cone, which is usually empty

Duality Theory and Applications to Unilateral Problems

GIUFFRE', Sofia;
2014

Abstract

This paper is concerned with the problem of strong duality between an infinite dimensional convex optimization problem with cone and equality constraints and its Lagrange dual. A necessary and sufficient condition and sufficient conditions, really new, in order that the strong duality holds true are given. As an application, the existence of the Lagrange multiplier associated with the obstacle problem and to an elastic–plastic torsion problem, more general than the ones Previously considered, is stated together with a characterization of the elastic–plastic torsion problem. This application is the main result of the paper. It is worth remarking that the usual conditions based on the interior, on the core, on the intrinsic core or on the strong quasi-relative interior cannot be used because they require the nonemptiness of the interior (and of the above mentioned generalized interior concepts) of the ordering cone, which is usually empty
File in 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: http://hdl.handle.net/20.500.12318/9254
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 23
  • ???jsp.display-item.citation.isi??? ND
social impact