Duality models for some nonclassical problems in the calculus of variations
type: Item
instance of: scholarly article
title: Duality models for some nonclassical problems in the calculus of variations
zbMATH Open document ID: 1033.49040
DOI: 10.1155/S0161171203303370
author: G. J. Zalmai
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2003-12-03T00:00:00Z
full work available at URL: https://eudml.org/doc/50656
review text: Summary: Parametric and nonparametric necessary and sufficient optimality conditions are established for a class of nonconvex variational problems with generalized fractional objective functions and nonlinear inequality constraints containing arbitrary norms. Based on these optimality criteria, ten parametric and parameter-free dual problems are constructed and appropriate duality theorems are proved. These optimality and duality results contain, as special cases, similar results for minmax fractional variational problems involving square roots of positive semidefinite quadratic forms as well as for variational problems with fractional, discrete max, and conventional objective functions, which are particular cases of the main problem considered in this paper. The duality models presented here subsume various existing duality formulations for variational problems and include variational generalizations of a great variety of cognate dual problems investigated previously in the area of finite-dimensional nonlinear programming by an assortment of ad hoc methods.
Mathematics Subject Classification ID: 49N15
Mathematics Subject Classification ID: 49K35
Mathematics Subject Classification ID: 90C32
Mathematics Subject Classification ID: 90C47
zbMATH DE Number: 2012671
zbMATH Keywords: nonparametric necessary and sufficient optimality condition
zbMATH Keywords: nonconvex variational problems
zbMATH Keywords: duality
zbMATH Keywords: minimax fractional variational problem
MaRDI profile type: Publication
OpenAlex ID: W2079082303
description: scientific article; zbMATH DE number 2012671