Duality Theory and Applications to Unilateral Problems

Patrizia Daniele (), Sofia Giuffrè (), Antonino Maugeri () and Fabio Raciti ()
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Patrizia Daniele: Università di Catania
Sofia Giuffrè: Mediterranean University of Reggio Calabria
Antonino Maugeri: Università di Catania
Fabio Raciti: Università di Catania

Journal of Optimization Theory and Applications, 2014, vol. 162, issue 3, No 3, 718-734

Abstract: 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.

Keywords: Strong duality; Variational inequalities; Quasi-relative interior; Elastic–plastic torsion (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-013-0512-4

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