On Infinite-Dimensional Convex Programs

One way to approach infinite-dimensional nonlinear programs is to append increasingly large cost or penalty terms to the objective function in such a way that the minima of the augmented but unconstrained functions converge to the constrained minimum in the limit. In this paper we establish the convergence of the penalty argument on reflexive B-spaces, and then apply it to obtain the Kuhn-Tucker necessary conditions for convex programs in Hillbert space. The proof is constructive and suggests a computationally feasible algorithm for solving such programs.