Ebook: Minimization Methods for Non-Differentiable Functions
Author: Naum Zuselevich Shor (auth.)
- Tags: Systems Theory Control, Calculus of Variations and Optimal Control, Optimization
- Series: Springer Series in Computational Mathematics 3
- Year: 1985
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages I-VIII
Introduction....Pages 1-5
Special Classes of Nondifferentiable Functions and Generalizations of the Concept of the Gradient....Pages 6-21
The Subgradient Method....Pages 22-47
Gradient-type Methods with Space Dilation....Pages 48-92
Applications of Methods for Nonsmooth Optimization to the Solution of Mathematical Programming Problems....Pages 93-149
Back Matter....Pages 150-164
Content:
Front Matter....Pages I-VIII
Introduction....Pages 1-5
Special Classes of Nondifferentiable Functions and Generalizations of the Concept of the Gradient....Pages 6-21
The Subgradient Method....Pages 22-47
Gradient-type Methods with Space Dilation....Pages 48-92
Applications of Methods for Nonsmooth Optimization to the Solution of Mathematical Programming Problems....Pages 93-149
Back Matter....Pages 150-164
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