Optimization of discrete inclusions with mixed constraints via locally adjoint mappings

This paper considers an optimization problem for discrete inclusions and inequalities simultaneously. Using convex and non-smooth analysis of set-valued mappings, the problem is reduced to the intersection problem of two mappings, one representing the dynamics and the other representing inequality-type constraints. The optimality conditions for such a problem are expressed by a locally adjoint mapping for the intersection of set-valued mappings, which is the sum of two locally adjoint mappings. In turn, this also requires calculating the argmaximum sets and subdifferentials of the Hamiltonian functions. At the end of the article, some applications in the Neumann and Neumann-Gale models of economic dynamics are demonstrated.