International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 4, Pages 673-679
Minimization of nonsmooth integral functionals
1National Technical University, Department of Mathematics, Athens 15773, Greece
2R.P.I., Department of Civil Engineering, Troy 12180-3590, New York, USA
Received 18 May 1989; Revised 28 February 1990
Copyright © 1992 Nikolaos S. Papageorgiou and Apostolos S. Papageorgiou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this paper we examine optimization problems involving multidimensional nonsmooth integral functionals defined on Sobolev spaces. We obtain necessary and sufficient conditions for optimality in convex, finite dimensional problems using techniques from convex analysis and in nonconvex, finite dimensional problems, using the subdifferential of Clarke. We also consider problems with infinite dimensional state space and we finally present two examples.