Optimization in Banach Spaces by Alexander J. Zaslavski

Author:Alexander J. Zaslavski
Language: eng
Format: epub
ISBN: 9783031126444
Publisher: Springer International Publishing

3. Nonconvex Optimization

Alexander J. Zaslavski1

(1)Department of Mathematics, The Technion – Israel Institute of Technology, Haifa, Israel

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.

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