International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 4, Pages 673-679
doi:10.1155/S0161171292000899
Minimization of nonsmooth integral functionals
Nikolaos S. Papageorgiou1
and Apostolos S. Papageorgiou2
1National Technical University, Department of Mathematics, Athens 15773, Greece
2R.P.I., Department of Civil Engineering, Troy 12180-3590, New York, USA
Abstract
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.