Iterative procedures for constrained and unilateral optimization problems

We study an iterative procedure of the "feasible direction" type for determining an "extremal" of a (nonconvex) optimization problem with unilateral constraints patterned on the unilateral problems of optimal control. We also investigate auxiliary procedures for determining inf\´ {??| (??,0)??A}, where A is a closed convex subset of a Hilbert space IR ?? H, and for finding a point s(q) in A nearest some given point q. The convergence of the basic procedure is with respect to the sup norm of C(T,IRm) while the convergence of the inner iterations is with respect to the Hilbert structure of an embedding space L2(??IRm).