Minimization Methods for Non-Differentiable Functions (Springer Series in Computational Mathematics)

N. Z. Shor

ISBN 10: 3642821200 / ISBN 13: 9783642821202

Edité par Springer Berlin Heidelberg, 2011

A propos de cet article

reprint edition. 172 pages. 9.25x6.10x0.39 inches. In Stock. N° de réf. du vendeur x-3642821200

Détails bibliographiques

Titre : Minimization Methods for Non-Differentiable ...

Éditeur : Springer Berlin Heidelberg

Date d'édition : 2011

Reliure : Paperback

Etat : Brand New

A propos de ce titre

Synopsis :

In recent years much attention has been given to the development of auto- matic systems of planning, design and control in various branches of the national economy. Quality of decisions is an issue which has come to the forefront, increasing the significance of optimization algorithms in math- ematical software packages for al, ltomatic systems of various levels and pur- poses. Methods for minimizing functions with discontinuous gradients are gaining in importance and the xperts in the computational methods of mathematical programming tend to agree that progress in the development of algorithms for minimizing nonsmooth functions is the key to the con- struction of efficient techniques for solving large scale problems. This monograph summarizes to a certain extent fifteen years of the author's work on developing generalized gradient methods for nonsmooth minimization. This work started in the department of economic cybernetics of the Institute of Cybernetics of the Ukrainian Academy of Sciences under the supervision of V.S. Mikhalevich, a member of the Ukrainian Academy of Sciences, in connection with the need for solutions to important, practical problems of optimal planning and design. In Chap. I we describe basic classes of nonsmooth functions that are dif- ferentiable almost everywhere, and analyze various ways of defining generalized gradient sets. In Chap. 2 we study in detail various versions of the su bgradient method, show their relation to the methods of Fejer-type approximations and briefly present the fundamentals of e-subgradient methods.