Sensitivity of Optimal Solutions to Control Problems for Second Order Evolution Subdifferential Inclusions

Sensitivity of Optimal Solutions to Control Problems for Second Order Evolution Subdifferential... In this paper the sensitivity of optimal solutions to control problems described by second order evolution subdifferential inclusions under perturbations of state relations and of cost functionals is investigated. First we establish a new existence result for a class of such inclusions. Then, based on the theory of sequential $$\Gamma $$ Γ -convergence we recall the abstract scheme concerning convergence of minimal values and minimizers. The abstract scheme works provided we can establish two properties: the Kuratowski convergence of solution sets for the state relations and some complementary $$\Gamma $$ Γ -convergence of the cost functionals. Then these two properties are implemented in the considered case. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Sensitivity of Optimal Solutions to Control Problems for Second Order Evolution Subdifferential Inclusions

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Publisher
Springer US
Copyright
Copyright © 2015 by Springer Science+Business Media New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-014-9262-4
Publisher site
See Article on Publisher Site

Abstract

In this paper the sensitivity of optimal solutions to control problems described by second order evolution subdifferential inclusions under perturbations of state relations and of cost functionals is investigated. First we establish a new existence result for a class of such inclusions. Then, based on the theory of sequential $$\Gamma $$ Γ -convergence we recall the abstract scheme concerning convergence of minimal values and minimizers. The abstract scheme works provided we can establish two properties: the Kuratowski convergence of solution sets for the state relations and some complementary $$\Gamma $$ Γ -convergence of the cost functionals. Then these two properties are implemented in the considered case.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Jun 1, 2015

References

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