Journal Article

Quadratic Pareto optimal control of parabolic equation with state‐control constraints and an infinite number of variables

G. M. Bahaa

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 20, issue 2, pages 167-178
Published in print June 2003 | ISSN: 0265-0754
Published online June 2003 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/20.2.167
Quadratic Pareto optimal control of parabolic equation with state‐control constraints and an infinite number of variables

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A distributed Pareto optimal control problem for the parabolic operator with an infinite number of variables is considered. The performance index has an integral form. Constraints on controls and on states are imposed. To obtain optimality conditions for the Neumann problem, the generalization of the Dubovitskii–Milyutin Theorem given by WALCZAK, S. (1984a) Folia Mathematica, 1, 187–196 and (1984b) J. Optimiz. Theory Appl., 42, 561–582, was applied.

Keywords: Pareto optimal control problems; parabolic operators with an infinite number of variables; Dubovitskii–Milyutin Theorem; conical approximations; optimality conditions

Journal Article.  0 words. 

Subjects: Mathematics

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