Generic existence of solutions of minimization problems with constraints (Q2782919)

The author considers two classes of minimization problems, with a functional constraint on a complete metric space and with a non-functional constraint on a Banach space. The space of all cost functions is equipped with an appropriate complete uniformity and existence of the solutions for most of these functions is proved. Namely, in the space of functions there exists a subset which is a countable intersection of open everywhere dense sets, such that for each cost function in this subset the corresponding minimization problem has a unique solution. The main results of the paper are obtained as a realization of a certain variational principle.