A Variational Principle for Problems with Functional Constraints

This is the authors' abstract. We don't add key points for this paper.

In this paper we show that in several important classes of optimization problems, like mathematical programming with k-smooth data, quadratic programming in a Hilbert space, convex programming in a Banach space, semi-infinite programming, and optimal control of linear systems with quadratic cost, most of the problems (in the Baire category sense) are well-posed. This is derived from a general variational principle for problems with functional constraints.