A generalization of the gradient projection method to extremal problems with preconvex constraints. (Q1395322)

In this paper the authors consider a generalization of a method designed for minimization of smooth functions for some cases of preconvex constraints. New numerical algorithms are presented, and their convergence in the sense of necessary extremal conditions is proved under some additional assumptions. The idea of the new method is that the projection problems on the iteration steps are solved for some auxiliary convex sets rather than for the initial set of constraints.