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Title: Nonlinear Programming Problems Associated with Closed Range Operators

Abstract

Necessary conditions for the optimality of a pair (y-bar, u-bar) with respect to a locally Lipschitz cost functional L(y,u) , subject to Ay + F(y) = Cu + B(u) , are given in terms of generalized gradients. Here A and C are densely defined, closed, linear operators on some Banach spaces, while F and B are (Frechet) differentiable maps, which are suitably related to A and C . Various examples and potential applications to nonlinear programming models and nonlinear optimal control of partial differential equations are also discussed.

Authors:
 [1];  [2];  [1]
  1. Department of Mathematics, Ohio University, Athens, OH 45701 (United States)
  2. Department of Mathematics, University of Iasi, Ro-6600 Iasi (Romania)
Publication Date:
OSTI Identifier:
21067541
Resource Type:
Journal Article
Journal Name:
Applied Mathematics and Optimization
Additional Journal Information:
Journal Volume: 40; Journal Issue: 2; Other Information: DOI: 10.1007/s002459900123; Copyright (c) 1999 Springer-Verlag New York Inc.; Article Copyright (c) Inc. 1999 Springer-Verlag New York; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0095-4616
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BANACH SPACE; MAPS; NONLINEAR PROBLEMS; NONLINEAR PROGRAMMING; OPTIMAL CONTROL; PARTIAL DIFFERENTIAL EQUATIONS

Citation Formats

Aizicovici, S., Motreanu, D., and Pavel, N. H. Nonlinear Programming Problems Associated with Closed Range Operators. United States: N. p., 1999. Web. doi:10.1007/S002459900123.
Aizicovici, S., Motreanu, D., & Pavel, N. H. Nonlinear Programming Problems Associated with Closed Range Operators. United States. doi:10.1007/S002459900123.
Aizicovici, S., Motreanu, D., and Pavel, N. H. Wed . "Nonlinear Programming Problems Associated with Closed Range Operators". United States. doi:10.1007/S002459900123.
@article{osti_21067541,
title = {Nonlinear Programming Problems Associated with Closed Range Operators},
author = {Aizicovici, S. and Motreanu, D. and Pavel, N. H.},
abstractNote = {Necessary conditions for the optimality of a pair (y-bar, u-bar) with respect to a locally Lipschitz cost functional L(y,u) , subject to Ay + F(y) = Cu + B(u) , are given in terms of generalized gradients. Here A and C are densely defined, closed, linear operators on some Banach spaces, while F and B are (Frechet) differentiable maps, which are suitably related to A and C . Various examples and potential applications to nonlinear programming models and nonlinear optimal control of partial differential equations are also discussed.},
doi = {10.1007/S002459900123},
journal = {Applied Mathematics and Optimization},
issn = {0095-4616},
number = 2,
volume = 40,
place = {United States},
year = {1999},
month = {9}
}