Constrained Vector-Valued Dynamic Game and Symmetric Duality for Multiobjective Variational Problems

A certain constrained vector-valued dynamic game is formulated and shown to be equivalent to a pair of multiobjective symmetric dual variational problems which have more general formulations than those studied earlier. A number of duality theorems, are established under suitable generalized convexity assumptions on the functionals. Selfduality reflecting symmetric dynamic games is investigated. The constrained vector-valued dynamic game is also regarded as equivalent to a pair of symmetric multiobjective dual variational problems with natural boundary conditions rather than fixed end points. Finally, it is indicated that our results can be considered as dynamic generalizations of those already existing in the literature. AMS-Mathematics Subject Classification: Primary 90C30, Secondary 90C11, 90C20, 90C26.