Nonconvex Optimization

Abstract

In this chapter, we study the algorithms for constrained nonconvex minimization problems in a general Banach space with Frechet differentiable objective functions. Our goal is to obtain a good approximate solution of the problem in the presence of computational errors. It is shown that the algorithm generates a good approximate solution, if the sequence of computational errors is bounded from above by a small constant. We obtain a number of convergence results under different conditions including a theorem with explicit estimations for computational errors.