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Stable Parametric Programming (Hardcover, 2001 ed.)
Loot Price: R2,988
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Stable Parametric Programming (Hardcover, 2001 ed.)
Series: Applied Optimization, 57
Expected to ship within 10 - 15 working days
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Optimality and stability are two important notions in applied
mathematics. This book is a study of these notions and their
relationship in linear and convex parametric programming models. It
begins with a survey of basic optimality conditions in nonlinear
programming. Then new results in convex programming, using LFS
functions, for single-objective, multi-objective, differentiable
and non-smooth programs are introduced. Parametric programming
models are studied using basic tools of point-to-set topology.
Stability of the models is introduced, essentially, as continuity
of the feasible set of decision variables under continuous
perturbations of the parameters. Perturbations that preserve this
continuity are regions of stability. It is shown how these regions
can be identified. The main results on stability are
characterizations of locally and globally optimal parameters for
stable and also for unstable perturbations. The results are
straightened for linear models and bi-level programs. Some of the
results are extended to abstract spaces after considering
parameters as controls'. Illustrations from diverse fields, such as
data envelopment analysis, management, von Stackelberg games of
market economy, and navigation problems are given and several case
studies are solved by finding optimal parameters. The book has been
written in an analytic spirit. Many results appear here for the
first time in book form. Audience: The book is written at the level
of a first-year graduate course in optimization for students with
varied backgrounds interested in modeling of real-life problems. It
is expected that the reader has been exposed to a prior elementary
course in optimization, such as linear or non-linear programming.
The last section of the book requires some knowledge of functional
analysis.
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