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Perturbation Theory In Mathematical Programming And Its Applications
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Book Synopsis Perturbation Theory in Mathematical Programming and Its Applications by : Evgenij S. Levitin
Download or read book Perturbation Theory in Mathematical Programming and Its Applications written by Evgenij S. Levitin and published by . This book was released on 1994-09-06 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the author's research of local parametric optimization in the finite-dimensional case. This book provides a clear and complete formulation of the main perturbation theory problems for finite-dimensional optimization as well as new mathematical methods to analyze these problems. Using a unified approach, the author has developed a general perturbation theory for finite-dimensional extremum problems. Within the framework of this theory, methods for studying perturbed problems in zero-, first- and second-order approximations have been developed.
Book Synopsis Analytic Perturbation Theory and Its Applications by : Konstantin E. Avrachenkov
Download or read book Analytic Perturbation Theory and Its Applications written by Konstantin E. Avrachenkov and published by SIAM. This book was released on 2013-12-11 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models are often used to describe complex phenomena such as climate change dynamics, stock market fluctuations, and the Internet. These models typically depend on estimated values of key parameters that determine system behavior. Hence it is important to know what happens when these values are changed. The study of single-parameter deviations provides a natural starting point for this analysis in many special settings in the sciences, engineering, and economics. The difference between the actual and nominal values of the perturbation parameter is small but unknown, and it is important to understand the asymptotic behavior of the system as the perturbation tends to zero. This is particularly true in applications with an apparent discontinuity in the limiting behavior?the so-called singularly perturbed problems. Analytic Perturbation Theory and Its Applications includes a comprehensive treatment of analytic perturbations of matrices, linear operators, and polynomial systems, particularly the singular perturbation of inverses and generalized inverses. It also offers original applications in Markov chains, Markov decision processes, optimization, and applications to Google PageRank? and the Hamiltonian cycle problem as well as input retrieval in linear control systems and a problem section in every chapter to aid in course preparation.
Book Synopsis Mathematical Programming with Data Perturbations by : Anthony V. Fiacco
Download or read book Mathematical Programming with Data Perturbations written by Anthony V. Fiacco and published by CRC Press. This book was released on 2020-09-23 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Programming with Data Perturbations by : Anthony V. Fiacco
Download or read book Mathematical Programming with Data Perturbations written by Anthony V. Fiacco and published by CRC Press. This book was released on 1997-09-19 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Perturbation Analysis of Optimization Problems by : J.Frederic Bonnans
Download or read book Perturbation Analysis of Optimization Problems written by J.Frederic Bonnans and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: A presentation of general results for discussing local optimality and computation of the expansion of value function and approximate solution of optimization problems, followed by their application to various fields, from physics to economics. The book is thus an opportunity for popularizing these techniques among researchers involved in other sciences, including users of optimization in a wide sense, in mechanics, physics, statistics, finance and economics. Of use to research professionals, including graduate students at an advanced level.
Book Synopsis Introduction to the Theory of Nonlinear Optimization by : Johannes Jahn
Download or read book Introduction to the Theory of Nonlinear Optimization written by Johannes Jahn and published by Springer Nature. This book was released on 2020-07-02 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as an introductory text to optimization theory in normed spaces and covers all areas of nonlinear optimization. It presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a basic knowledge of linear functional analysis.
Book Synopsis Nonsmooth Equations in Optimization by : Diethard Klatte
Download or read book Nonsmooth Equations in Optimization written by Diethard Klatte and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Convex Analysis and Monotone Operator Theory in Hilbert Spaces by : Heinz H. Bauschke
Download or read book Convex Analysis and Monotone Operator Theory in Hilbert Spaces written by Heinz H. Bauschke and published by Springer. This book was released on 2017-02-28 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, machine learning, physics, decision sciences, economics, and inverse problems. The second edition of Convex Analysis and Monotone Operator Theory in Hilbert Spaces greatly expands on the first edition, containing over 140 pages of new material, over 270 new results, and more than 100 new exercises. It features a new chapter on proximity operators including two sections on proximity operators of matrix functions, in addition to several new sections distributed throughout the original chapters. Many existing results have been improved, and the list of references has been updated. Heinz H. Bauschke is a Full Professor of Mathematics at the Kelowna campus of the University of British Columbia, Canada. Patrick L. Combettes, IEEE Fellow, was on the faculty of the City University of New York and of Université Pierre et Marie Curie – Paris 6 before joining North Carolina State University as a Distinguished Professor of Mathematics in 2016.
Book Synopsis Stable Parametric Programming by : S. Zlobec
Download or read book Stable Parametric Programming written by S. Zlobec and published by Springer Science & Business Media. This book was released on 2001-08-31 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Recent Advances in Optimization by : Peter Gritzmann
Download or read book Recent Advances in Optimization written by Peter Gritzmann and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent theoretical and practical aspects in the field of optimization and convex analysis. The topics covered in this volume include: - Equilibrium models in economics. - Control theory and semi-infinite programming. - Ill-posed variational problems. - Global optimization. - Variational methods in image restoration. - Nonsmooth optimization. - Duality theory in convex and nonconvex optimization. - Methods for large scale problems.
Book Synopsis Theory of Linear Optimization by : Ivan Ivanovich Eremin
Download or read book Theory of Linear Optimization written by Ivan Ivanovich Eremin and published by VSP. This book was released on 2002-01-01 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the basic component of the theory of linear optimisation problems: systems of linear inequalities. Such an approach is exact in both a historical and methodological sense.In the first two chapters attention focuses on economic interpretation of models, theorems, and approaches. The other chapters are dedicated to less traditional problems of linear optimisation, such as improper problems and duality, lexicographic problems and duality, piecewise linear problems and duality, etc. The book also covers some general methods for calculating processes for certain problems of linear optimisation: the problem of stability and correctness.This book contains original scientific material, which is of value and interest to students and specialists in mathematical optimisation, operation research, economic-mathematical modelling and related disciplines.
Book Synopsis Applied Analysis by : James Robert Dorroh
Download or read book Applied Analysis written by James Robert Dorroh and published by American Mathematical Soc.. This book was released on 1999 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains proceedings from the AMS conference on Applied Analysis held at LSU (Baton Rouge) in April 1996. Topics include partial differential equations, spectral theory, functional analysis and operator theory, complex analysis, numerical analysis and related mathematics. Applications include quantum theory, fluid dynamics, control theory and abstract issues, such as well-posedness, asymptotics, and more. The book presents the scope and depth of the conference and its lectures. The state-of-the-art surveys by Jerry Bona and Fritz Gesztesy contain topics of wide interest. There have been a number of good conferences on related topics, yet this volume offers readers a unique varied viewpoint. The scope of the material in the book will benefit readers approaching the work from diverse perspectives. It will serve those seeking motivational scientific problems, those interested in techniques and subspecialities and those looking for current results in the field
Book Synopsis Optimization Theory by : Hubertus Th. Jongen
Download or read book Optimization Theory written by Hubertus Th. Jongen and published by Springer Science & Business Media. This book was released on 2007-05-08 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a comprehensive introduction to the theory of (deterministic) optimization. It covers both continuous and discrete optimization. This allows readers to study problems under different points-of-view, which supports a better understanding of the entire field. Many exercises are included to increase the reader's understanding.
Book Synopsis Mathematical Demoeconomy by : Yuri S. Popkov
Download or read book Mathematical Demoeconomy written by Yuri S. Popkov and published by Walter de Gruyter. This book was released on 2014-04-02 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph aspires to lay the foundations of a new scientific discipline, demoeconomics, representing the synthesis of demography and spatial economics. This synthesis is performed in terms of interaction between population and its economic activity. The monograph appears a unique research work having no analogs in scientific literature. Demoeconomic systems are studied involving the macrosystems approach which combines the generalized entropy maximization principle and the local equilibria principle. Demoeconomic systems operate in an uncertain environment; thus and so, the monograph develops the methodology and technique of probabilistic modeling and forecasting of their evolution.
Book Synopsis Foundations of Bilevel Programming by : Stephan Dempe
Download or read book Foundations of Bilevel Programming written by Stephan Dempe and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bilevel programming problems are hierarchical optimization problems where the constraints of one problem (the so-called upper level problem) are defined in part by a second parametric optimization problem (the lower level problem). If the lower level problem has a unique optimal solution for all parameter values, this problem is equivalent to a one-level optimization problem having an implicitly defined objective function. Special emphasize in the book is on problems having non-unique lower level optimal solutions, the optimistic (or weak) and the pessimistic (or strong) approaches are discussed. The book starts with the required results in parametric nonlinear optimization. This is followed by the main theoretical results including necessary and sufficient optimality conditions and solution algorithms for bilevel problems. Stationarity conditions can be applied to the lower level problem to transform the optimistic bilevel programming problem into a one-level problem. Properties of the resulting problem are highlighted and its relation to the bilevel problem is investigated. Stability properties, numerical complexity, and problems having additional integrality conditions on the variables are also discussed. Audience: Applied mathematicians and economists working in optimization, operations research, and economic modelling. Students interested in optimization will also find this book useful.
Author :Christodoulos A. Floudas Publisher :Springer Science & Business Media ISBN 13 :1461334373 Total Pages :638 pages Book Rating :4.4/5 (613 download)
Book Synopsis State of the Art in Global Optimization by : Christodoulos A. Floudas
Download or read book State of the Art in Global Optimization written by Christodoulos A. Floudas and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization problems abound in most fields of science, engineering, and tech nology. In many of these problems it is necessary to compute the global optimum (or a good approximation) of a multivariable function. The variables that define the function to be optimized can be continuous and/or discrete and, in addition, many times satisfy certain constraints. Global optimization problems belong to the complexity class of NP-hard prob lems. Such problems are very difficult to solve. Traditional descent optimization algorithms based on local information are not adequate for solving these problems. In most cases of practical interest the number of local optima increases, on the aver age, exponentially with the size of the problem (number of variables). Furthermore, most of the traditional approaches fail to escape from a local optimum in order to continue the search for the global solution. Global optimization has received a lot of attention in the past ten years, due to the success of new algorithms for solving large classes of problems from diverse areas such as engineering design and control, computational chemistry and biology, structural optimization, computer science, operations research, and economics. This book contains refereed invited papers presented at the conference on "State of the Art in Global Optimization: Computational Methods and Applications" held at Princeton University, April 28-30, 1995. The conference presented current re search on global optimization and related applications in science and engineering. The papers included in this book cover a wide spectrum of approaches for solving global optimization problems and applications.
Book Synopsis Differential Geometry and Control by : Guillermo Segundo Ferreyra
Download or read book Differential Geometry and Control written by Guillermo Segundo Ferreyra and published by American Mathematical Soc.. This book was released on 1999 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains papers from a summer 1997 meeting on recent developments and important open problems in geometric control theory. Topics include linear control systems in Lie groups and controllability, real analytic geometry and local observability, singular extremals of order 3 and chattering, infinite time horizon stochastic control problems in hyperbolic three space, and Monge-Ampere equations. No index. Annotation copyrighted by Book News, Inc., Portland, OR.
