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- DescriptionOptimality and stability are two important tions in applied mathematics. This book is a study of these tions and their relationship in linear and convex parametric programming models. It begins with a survey of basic optimality conditions in nlinear programming. Then new results in convex programming, using LFS functions, for single-objective, multi-objective, differentiable and n-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 ecomy, 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 n-linear programming. The last section of the book requires some kwledge of functional analysis.
- Author(s)Sanjo Zlobec
- PublisherSpringer-Verlag New York Inc.
- Date of Publication26/11/2013
- SubjectManagement & Business: General
- Series TitleApplied Optimization
- Series Part/Volume Number57
- Place of PublicationNew York, NY
- Country of PublicationUnited States
- ImprintSpringer-Verlag New York Inc.
- Content Notebiography
- Weight534 g
- Width155 mm
- Height235 mm
- Spine18 mm
- Edition StatementSoftcover reprint of the original 1st ed. 2001
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