On Equivalence of the Method of Steepest Descent and the Method of Hypodifferential Descent in Some Constrained Optimization Problems

The method of exact penalty functions is widely used for the study of constrained optimization problems. The approach based on exact penalization was successfully applied to the study of optimal control problems and various problems of the calculus of variations, computational geometry and mathematical diagnostics. It is worth mentioning that even if the constrained optimization problem under consideration is smooth, the equivalent unconstrained optimization problems constructed via exact penalization technique is essentially nonsmooth. In this paper, we study infinite dimensional optimization problems with linear constraints with the use of the theory of exact penalty functions. We consider the method of steepest descent and the method of hypodifferential descent for this type of problems. We obtain some properties of these methods and study the cases when they coincide.