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Nonsmooth Equations in Optimization - Regularity, Calculus, Methods and Applications (Hardcover, 2002 ed.)
Loot Price: R4,560
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Nonsmooth Equations in Optimization - Regularity, Calculus, Methods and Applications (Hardcover, 2002 ed.)
Series: Nonconvex Optimization and Its Applications, 60
Expected to ship within 10 - 15 working days
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Many questions dealing with solvability, stability and solution
methods for va- ational inequalities or equilibrium, optimization
and complementarity problems lead to the analysis of certain
(perturbed) equations. This often requires a - formulation of the
initial model being under consideration. Due to the specific of the
original problem, the resulting equation is usually either not
differ- tiable (even if the data of the original model are smooth),
or it does not satisfy the assumptions of the classical implicit
function theorem. This phenomenon is the main reason why a
considerable analytical inst- ment dealing with generalized
equations (i.e., with finding zeros of multivalued mappings) and
nonsmooth equations (i.e., the defining functions are not c-
tinuously differentiable) has been developed during the last 20
years, and that under very different viewpoints and assumptions. In
this theory, the classical hypotheses of convex analysis, in
particular, monotonicity and convexity, have been weakened or
dropped, and the scope of possible applications seems to be quite
large. Briefly, this discipline is often called nonsmooth analysis,
sometimes also variational analysis. Our book fits into this
discipline, however, our main intention is to develop the
analytical theory in close connection with the needs of
applications in optimization and related subjects. Main Topics of
the Book 1. Extended analysis of Lipschitz functions and their
generalized derivatives, including "Newton maps" and regularity of
multivalued mappings. 2. Principle of successive approximation
under metric regularity and its - plication to implicit functions.
General
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