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Author: Refugio Trujillo-Cortez
Publisher:
Published: 2000
Total Pages: 312
ISBN-13:
DOWNLOAD EBOOK"The results on stability are applied for bilevel convex models and an algorithm for solving these models, based on a marginal value formula, is suggested and then applied to a real-life problem in the petroleum industry." --
Author: S. Zlobec
Publisher: Springer Science & Business Media
Published: 2013-11-21
Total Pages: 329
ISBN-13: 1461500117
DOWNLOAD EBOOKOptimality 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.
Author: Li Li
Publisher: Springer
Published: 2015-03-26
Total Pages: 150
ISBN-13: 3662463563
DOWNLOAD EBOOKThis book focuses on the applications of convex optimization and highlights several topics, including support vector machines, parameter estimation, norm approximation and regularization, semi-definite programming problems, convex relaxation, and geometric problems. All derivation processes are presented in detail to aid in comprehension. The book offers concrete guidance, helping readers recognize and formulate convex optimization problems they might encounter in practice.
Author: Aharon Ben-Tal
Publisher: SIAM
Published: 2001-01-01
Total Pages: 500
ISBN-13: 0898714915
DOWNLOAD EBOOKHere is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming. The authors present the basic theory underlying these problems as well as their numerous applications in engineering, including synthesis of filters, Lyapunov stability analysis, and structural design. The authors also discuss the complexity issues and provide an overview of the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming. The book's focus on well-structured convex problems in conic form allows for unified theoretical and algorithmical treatment of a wide spectrum of important optimization problems arising in applications.
Author: Yeol Je Cho
Publisher: Nova Publishers
Published: 2004
Total Pages: 240
ISBN-13: 9781590338902
DOWNLOAD EBOOKFixed Point Theory & Applications, Volume 5
Author: Fiacco
Publisher: Academic Press
Published: 1983-11-02
Total Pages: 381
ISBN-13: 0080956718
DOWNLOAD EBOOKIntroduction to Sensitivity and Stability Analysis in Nonlinear Programming
Author: Yurii Nesterov
Publisher: SIAM
Published: 1994-01-01
Total Pages: 414
ISBN-13: 9781611970791
DOWNLOAD EBOOKSpecialists working in the areas of optimization, mathematical programming, or control theory will find this book invaluable for studying interior-point methods for linear and quadratic programming, polynomial-time methods for nonlinear convex programming, and efficient computational methods for control problems and variational inequalities. A background in linear algebra and mathematical programming is necessary to understand the book. The detailed proofs and lack of "numerical examples" might suggest that the book is of limited value to the reader interested in the practical aspects of convex optimization, but nothing could be further from the truth. An entire chapter is devoted to potential reduction methods precisely because of their great efficiency in practice.
Author: Christodoulos A. Floudas
Publisher: Springer Science & Business Media
Published: 2008-09-04
Total Pages: 4646
ISBN-13: 0387747583
DOWNLOAD EBOOKThe goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".
Author: Andrew Eberhard
Publisher: Springer Science & Business Media
Published: 2006-06-22
Total Pages: 342
ISBN-13: 0387236392
DOWNLOAD EBOOKIn recent years there is a growing interest in generalized convex fu- tions and generalized monotone mappings among the researchers of - plied mathematics and other sciences. This is due to the fact that mathematical models with these functions are more suitable to describe problems of the real world than models using conventional convex and monotone functions. Generalized convexity and monotonicity are now considered as an independent branch of applied mathematics with a wide range of applications in mechanics, economics, engineering, finance and many others. The present volume contains 20 full length papers which reflect c- rent theoretical studies of generalized convexity and monotonicity, and numerous applications in optimization, variational inequalities, equil- rium problems etc. All these papers were refereed and carefully selected from invited talks and contributed talks that were presented at the 7th International Symposium on Generalized Convexity/Monotonicity held in Hanoi, Vietnam, August 27-31, 2002. This series of Symposia is or- nized by the Working Group on Generalized Convexity (WGGC) every 3 years and aims to promote and disseminate research on the field. The WGGC (http://www.genconv.org) consists of more than 300 researchers coming from 36 countries.
Author: J.Frederic Bonnans
Publisher: Springer Science & Business Media
Published: 2013-11-22
Total Pages: 618
ISBN-13: 1461213940
DOWNLOAD EBOOKA 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.
