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Books > Reference & Interdisciplinary > Communication studies > Information theory > Cybernetics & systems theory
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Minimization Methods for Non-Differentiable Functions (Paperback, Softcover reprint of the original 1st ed. 1985)
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Minimization Methods for Non-Differentiable Functions (Paperback, Softcover reprint of the original 1st ed. 1985)
Series: Springer Series in Computational Mathematics, 3
Expected to ship within 18 - 22 working days
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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."
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