A necessary and sufficient condition of optimality for a class of multidimensional control problems

In this paper, we introduce a necessary and sufficient condition of optimality for a new class of multidimensional optimal control problems governed by path-independent curvilinear integral functionals and mixed constraints involving first-order partial differential equations (PDEs) ofm-flow type. Furthermore, as a consequence, we establish the equivalence between the class of (strongly)b-invex functionals and the class of (strongly)b-pseudoinvex functionals. The mathematical development in the paper is supported by illustrative examples, as well.