Nonsmooth Optimization

In the classical Mathematical Analysis, the functions under study are, mostly, differentiable. Nonsmooth Analysis came into being in the 60’s of the XXth century. Its appearance was requested by practical problems of industry, airspace engineering, economics, other sciences where nonsmooth mathemati...

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Bibliographic Details
Published inNonlinear Optimization Vol. 1989; pp. 55 - 163
Main Authors Fletcher, Roger, Demyanov, Vladimir F, Bomze, Immanuel M, Terlaky, Tamás
Format Book Chapter
LanguageEnglish
Published Germany Springer Berlin / Heidelberg 2010
Springer Berlin Heidelberg
SeriesLecture Notes in Mathematics
Subjects
Constrain Optimization Problem
Directional Derivative
Exact Penalty
Nonsmooth Analysis
Penalty Function
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Summary:In the classical Mathematical Analysis, the functions under study are, mostly, differentiable. Nonsmooth Analysis came into being in the 60’s of the XXth century. Its appearance was requested by practical problems of industry, airspace engineering, economics, other sciences where nonsmooth mathematical models were employed to describe more adequately the processes to be investigated. One of the most important problems in Mathematical Analysis is that of finding extremal values of a functional. The same is true in Nonsmooth Analysis. In the present notes, the problem of finding extremal values of a functional defined on some space is discussed. If there are no constraints on the variables, the problem is called the unconstrained optimization problem. If constraints are present, the problem becomes the constrained optimization one.
ISBN:9783642113383
3642113389
ISSN:0075-8434
1617-9692
DOI:10.1007/978-3-642-11339-0_2