Mathematical Programming with Data Perturbations

by Anthony V. Fiacco (Editor)

Overview

Presents research contributions and tutorial expositions on current methodologies for sensitivity, stability and approximation analyses of mathematical programming and related problem structures involving parameters. The text features up-to-date findings on important topics, covering such areas as the effect of perturbations on the performance of algorithms, approximation techniques for optimal control problems, and global error bounds for convex inequalities.

Product Details

ISBN-13:	9781000153668
Publisher:	CRC Press
Publication date:	09/23/2020
Series:	Lecture Notes in Pure and Applied Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	456
File size:	18 MB
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About the Author

ANTHONY V. FIACCO is Professor Emeritus of Operations Research and Applied Science at George Washington University, Washington, D.C. From 1960 to 1971, Dr. Fiacco was an Operations Analyst for the Research Analysis Corporation in McLean, Virginia, where he was Project Chairman of a study that pioneered several breakthroughs in nonlinear programming (NLP) methodology. He is the author or coauthor of numerous papers on NLP theory and applications, the coauthor with Garth P. McCormick in 1968 of a Lanchester prize-winning book on barrier and penalty function methodology, and the editor of several books, including Mathematical Programming with Data Perturbations I and II (both titles, Marcel Dekker, Inc.). A prominent contributor to the development of computable methods for sensitivity and stability analysis, Dr. Fiacco received the Ph.D. degree 1967 in applied mathematics from Northwestern University, Evanston, Illinois. Since 1979, he has organized, at the George Washington University, the only annual conference completely devoted to sensitivity and stability issues.

Table of Contents

Preface -- Contributors -- Discretization and Mesh-Independence of Newton’s Method for Generalized Equations /Walter Alt -- Extended Quadratic Tangent Optimization Problems /J. F. Bonnans -- On Generalized Differentiability of Optimal Solutions in Nonlinear Parametric Optimization /S. Dempe -- Characterizations of Lipschitzian Stability in Nonlinear Programming /A. L. Dontchev and R. T. Rockafellar -- On Second Order Sufficient Conditions for Structured Nonlinear Programs in Infinite-Dimensional Function Spaces /J. C. Dunn -- Algorithmic Stability Analysis for Certain Trust Region Methods /Ursula Felgenhauer -- A Note on Using Linear Knowledge to Solve Efficiently Linear Programs Specified with Approximate Data /Sharon Filipowski -- On the Role of the Mangasarian-Fromovitz Constraint Qualification for Penalty-, Exact Penalty-, and Lagrange Multiplier Methods /Jurgen Guddat, Francisco Guerra, and Dieter Nowack -- Hoffman’s Error Bound for Systems of Convex Inequalities /Diethard Klatte -- Lipschitzian and Pseudo-Lipschitzian Inverse Functions and Applications to Nonlinear Optimization /Bernd Kummer -- On Well-Posedness and Stability Analysis in Optimization /R. Lucchetti and T. Zolezzi -- Convergence of Approximations to Nonlinear Optimal Control Problems /Kazimierz Malanowski, Christof Bits kens, and Helmut Maurer -- A Perturbation-Based Duality Classification for Max-Flow Min-Cut Problems of Strang and Iri /Ryohei Nozawa and K. O. Kortanek -- Central and Peripheral Results in the Study of Marginal and Performance Functions? /Jean-Paul Penot -- Topological Stability of Feasible Sets in Semi-infinite Optimization: A Tutorial /Jan-J. Riickmann -- Solution Existence for Infinite Quadratic Programming /I. E. Schochetman, R. L. Smith, and S. K. Tsui -- Sensitivity Analysis of Nonlinear Programming Problems via Minimax Functions /S. Shiraishi -- Parametric Linear Complementarity Problems /Klaus Tammer -- Sufficient Conditions for Weak Sharp Minima of Order Two and Directional Derivatives of the Value Function /Doug Ward -- Index.

Editorial Reviews

Expanded from the proceedings of a May 1995 symposium on operations research in Washington, DC to include tutorials and reports of current research from contributors throughout the world. Integrates many of the best known classical results into the modern context and often as a special case of current results. Among the areas addressed are new characterizations of regularity, the effect of perturbations on the performance of algorithms, using approximation techniques to derive optimality and regularity conditions, strong and weak second-order conditions and the attendant differential stability results of first and second orders, duality classification using perturbation techniques, embedding and path-following methods, and relations between computational efficiency and data structure and between constraint qualification and error bounds and regularity. Two other volumes in the series are derived from the symposium and carry the same title. Reproduced from typescripts. No index. Annotation c. by Book News, Inc., Portland, Or.

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