Foundations Of Mathematical Optimization

Author : Diethard Ernst Pallaschke,S. Rolewicz
Publisher : Springer Science & Business Media
Page : 597 pages
File Size : 53,6 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401715881

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Foundations of Mathematical Optimization by Diethard Ernst Pallaschke,S. Rolewicz Pdf

Many books on optimization consider only finite dimensional spaces. This volume is unique in its emphasis: the first three chapters develop optimization in spaces without linear structure, and the analog of convex analysis is constructed for this case. Many new results have been proved specially for this publication. In the following chapters optimization in infinite topological and normed vector spaces is considered. The novelty consists in using the drop property for weak well-posedness of linear problems in Banach spaces and in a unified approach (by means of the Dolecki approximation) to necessary conditions of optimality. The method of reduction of constraints for sufficient conditions of optimality is presented. The book contains an introduction to non-differentiable and vector optimization. Audience: This volume will be of interest to mathematicians, engineers, and economists working in mathematical optimization.

Author : Osman Güler
Publisher : Springer Science & Business Media
Page : 445 pages
File Size : 55,5 Mb
Release : 2010-08-03
Category : Business & Economics
ISBN : 9780387684079

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Foundations of Optimization by Osman Güler Pdf

This book covers the fundamental principles of optimization in finite dimensions. It develops the necessary material in multivariable calculus both with coordinates and coordinate-free, so recent developments such as semidefinite programming can be dealt with.

Author : Diethard Pallaschke,Stefan Rolewicz
Publisher : Unknown
Page : 600 pages
File Size : 49,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 9401715890

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Foundations of Mathematical Optimization by Diethard Pallaschke,Stefan Rolewicz Pdf

Author : Douglass J. Wilde,Charles S. Beightler
Publisher : Unknown
Page : 504 pages
File Size : 52,5 Mb
Release : 1967
Category : Mathematical optimization
ISBN : UOM:39015001318263

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Foundations of Optimization by Douglass J. Wilde,Charles S. Beightler Pdf

Author : M. S. Bazaraa,C. M. Shetty
Publisher : Springer Science & Business Media
Page : 203 pages
File Size : 53,6 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642482946

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Foundations of Optimization by M. S. Bazaraa,C. M. Shetty Pdf

Current1y there is a vast amount of literature on nonlinear programming in finite dimensions. The pub1ications deal with convex analysis and severa1 aspects of optimization. On the conditions of optima1ity they deal mainly with generali- tions of known results to more general problems and also with less restrictive assumptions. There are also more general results dealing with duality. There are yet other important publications dealing with algorithmic deve10pment and their applications. This book is intended for researchers in nonlinear programming, and deals mainly with convex analysis, optimality conditions and duality in nonlinear programming. It consolidates the classic results in this area and some of the recent results. The book has been divided into two parts. The first part gives a very comp- hensive background material. Assuming a background of matrix algebra and a senior level course in Analysis, the first part on convex analysis is self-contained, and develops some important results needed for subsequent chapters. The second part deals with optimality conditions and duality. The results are developed using extensively the properties of cones discussed in the first part. This has faci- tated derivations of optimality conditions for equality and inequality constrained problems. Further, minimum-principle type conditions are derived under less restrictive assumptions. We also discuss constraint qualifications and treat some of the more general duality theory in nonlinear programming.

Author : Ding-Zhu Du,Panos M. Pardalos,Weili Wu
Publisher : Springer Science & Business Media
Page : 277 pages
File Size : 51,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475757958

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Mathematical Theory of Optimization by Ding-Zhu Du,Panos M. Pardalos,Weili Wu Pdf

This book provides an introduction to the mathematical theory of optimization. It emphasizes the convergence theory of nonlinear optimization algorithms and applications of nonlinear optimization to combinatorial optimization. Mathematical Theory of Optimization includes recent developments in global convergence, the Powell conjecture, semidefinite programming, and relaxation techniques for designs of approximation solutions of combinatorial optimization problems.

Author : Xin-She Yang,Xing-Shi He
Publisher : Springer
Page : 107 pages
File Size : 46,6 Mb
Release : 2019-05-08
Category : Mathematics
ISBN : 9783030169367

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Mathematical Foundations of Nature-Inspired Algorithms by Xin-She Yang,Xing-Shi He Pdf

This book presents a systematic approach to analyze nature-inspired algorithms. Beginning with an introduction to optimization methods and algorithms, this book moves on to provide a unified framework of mathematical analysis for convergence and stability. Specific nature-inspired algorithms include: swarm intelligence, ant colony optimization, particle swarm optimization, bee-inspired algorithms, bat algorithm, firefly algorithm, and cuckoo search. Algorithms are analyzed from a wide spectrum of theories and frameworks to offer insight to the main characteristics of algorithms and understand how and why they work for solving optimization problems. In-depth mathematical analyses are carried out for different perspectives, including complexity theory, fixed point theory, dynamical systems, self-organization, Bayesian framework, Markov chain framework, filter theory, statistical learning, and statistical measures. Students and researchers in optimization, operations research, artificial intelligence, data mining, machine learning, computer science, and management sciences will see the pros and cons of a variety of algorithms through detailed examples and a comparison of algorithms.

Author : Niclas Andreasson,Anton Evgrafov,Michael Patriksson
Publisher : Courier Dover Publications
Page : 515 pages
File Size : 42,7 Mb
Release : 2020-01-15
Category : Mathematics
ISBN : 9780486802879

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An Introduction to Continuous Optimization by Niclas Andreasson,Anton Evgrafov,Michael Patriksson Pdf

This treatment focuses on the analysis and algebra underlying the workings of convexity and duality and necessary/sufficient local/global optimality conditions for unconstrained and constrained optimization problems. 2015 edition.

Author : Michael J. Panik
Publisher : CRC Press
Page : 343 pages
File Size : 41,8 Mb
Release : 2021-09-30
Category : Mathematics
ISBN : 9781000408843

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Mathematical Analysis and Optimization for Economists by Michael J. Panik Pdf

In Mathematical Analysis and Optimization for Economists, the author aims to introduce students of economics to the power and versatility of traditional as well as contemporary methodologies in mathematics and optimization theory; and, illustrates how these techniques can be applied in solving microeconomic problems. This book combines the areas of intermediate to advanced mathematics, optimization, and microeconomic decision making, and is suitable for advanced undergraduates and first-year graduate students. This text is highly readable, with all concepts fully defined, and contains numerous detailed example problems in both mathematics and microeconomic applications. Each section contains some standard, as well as more thoughtful and challenging, exercises. Solutions can be downloaded from the CRC Press website. All solutions are detailed and complete. Features Contains a whole spectrum of modern applicable mathematical techniques, many of which are not found in other books of this type. Comprehensive and contains numerous and detailed example problems in both mathematics and economic analysis. Suitable for economists and economics students with only a minimal mathematical background. Classroom-tested over the years when the author was actively teaching at the University of Hartford. Serves as a beginner text in optimization for applied mathematics students. Accompanied by several electronic chapters on linear algebra and matrix theory, nonsmooth optimization, economic efficiency, and distance functions available for free on www.routledge.com/9780367759018.

Author : Jeffrey Humpherys,Tyler J. Jarvis
Publisher : SIAM
Page : 806 pages
File Size : 54,6 Mb
Release : 2020-03-10
Category : Mathematics
ISBN : 9781611976069

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Foundations of Applied Mathematics, Volume 2 by Jeffrey Humpherys,Tyler J. Jarvis Pdf

In this second book of what will be a four-volume series, the authors present, in a mathematically rigorous way, the essential foundations of both the theory and practice of algorithms, approximation, and optimization—essential topics in modern applied and computational mathematics. This material is the introductory framework upon which algorithm analysis, optimization, probability, statistics, machine learning, and control theory are built. This text gives a unified treatment of several topics that do not usually appear together: the theory and analysis of algorithms for mathematicians and data science students; probability and its applications; the theory and applications of approximation, including Fourier series, wavelets, and polynomial approximation; and the theory and practice of optimization, including dynamic optimization. When used in concert with the free supplemental lab materials, Foundations of Applied Mathematics, Volume 2: Algorithms, Approximation, Optimization teaches not only the theory but also the computational practice of modern mathematical methods. Exercises and examples build upon each other in a way that continually reinforces previous ideas, allowing students to retain learned concepts while achieving a greater depth. The mathematically rigorous lab content guides students to technical proficiency and answers the age-old question “When am I going to use this?” This textbook is geared toward advanced undergraduate and beginning graduate students in mathematics, data science, and machine learning.

Author : R. Lowen,A. Verschoren
Publisher : Springer Science & Business Media
Page : 463 pages
File Size : 48,6 Mb
Release : 2007-10-27
Category : Mathematics
ISBN : 9781402066689

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Foundations of Generic Optimization by R. Lowen,A. Verschoren Pdf

This is a comprehensive overview of the basics of fuzzy control, which also brings together some recent research results in soft computing, in particular fuzzy logic using genetic algorithms and neural networks. This book offers researchers not only a solid background but also a snapshot of the current state of the art in this field.

Author : Jan Snyman
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 52,8 Mb
Release : 2005-12-15
Category : Mathematics
ISBN : 9780387243498

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Practical Mathematical Optimization by Jan Snyman Pdf

This book presents basic optimization principles and gradient-based algorithms to a general audience, in a brief and easy-to-read form. It enables professionals to apply optimization theory to engineering, physics, chemistry, or business economics.

Author : H. Ronald Miller
Publisher : John Wiley & Sons
Page : 676 pages
File Size : 49,9 Mb
Release : 2011-03-29
Category : Mathematics
ISBN : 9781118031186

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Optimization by H. Ronald Miller Pdf

A thorough and highly accessible resource for analysts in a broadrange of social sciences. Optimization: Foundations and Applications presents a series ofapproaches to the challenges faced by analysts who must find thebest way to accomplish particular objectives, usually with theadded complication of constraints on the available choices.Award-winning educator Ronald E. Miller provides detailed coverageof both classical, calculus-based approaches and newer,computer-based iterative methods. Dr. Miller lays a solid foundation for both linear and nonlinearmodels and quickly moves on to discuss applications, includingiterative methods for root-finding and for unconstrainedmaximization, approaches to the inequality constrained linearprogramming problem, and the complexities of inequality constrainedmaximization and minimization in nonlinear problems. Otherimportant features include: More than 200 geometric interpretations of algebraic results,emphasizing the intuitive appeal of mathematics Classic results mixed with modern numerical methods to aidusers of computer programs Extensive appendices containing mathematical details importantfor a thorough understanding of the topic With special emphasis on questions most frequently asked by thoseencountering this material for the first time, Optimization:Foundations and Applications is an extremely useful resource forprofessionals in such areas as mathematics, engineering, economicsand business, regional science, geography, sociology, politicalscience, management and decision sciences, public policy analysis,and numerous other social sciences. An Instructor's Manual presenting detailed solutions to all theproblems in the book is available upon request from the Wileyeditorial department.

Author : Stephen Boyd,Lieven Vandenberghe
Publisher : Cambridge University Press
Page : 744 pages
File Size : 50,9 Mb
Release : 2004-03-08
Category : Mathematics
ISBN : 9781107394001

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Convex Optimization by Stephen Boyd,Lieven Vandenberghe Pdf

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.

Author : Roman A. Polyak
Publisher : Springer Nature
Page : 552 pages
File Size : 51,6 Mb
Release : 2021-04-29
Category : Mathematics
ISBN : 9783030687137

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Introduction to Continuous Optimization by Roman A. Polyak Pdf

This self-contained monograph presents the reader with an authoritative view of Continuous Optimization, an area of mathematical optimization that has experienced major developments during the past 40 years. The book contains results which have not yet been covered in a systematic way as well as a summary of results on NR theory and methods developed over the last several decades. The readership is aimed to graduate students in applied mathematics, computer science, economics, as well as researchers working in optimization and those applying optimization methods for solving real life problems. Sufficient exercises throughout provide graduate students and instructors with practical utility in a two-semester course in Continuous Optimization. The topical coverage includes interior point methods, self-concordance theory and related complexity issues, first and second order methods with accelerated convergence, nonlinear rescaling (NR) theory and exterior point methods, just to mention a few. The book contains a unified approach to both interior and exterior point methods with emphasis of the crucial duality role. One of the main achievements of the book shows what makes the exterior point methods numerically attractive and why. The book is composed in five parts. The first part contains the basics of calculus, convex analysis, elements of unconstrained optimization, as well as classical results of linear and convex optimization. The second part contains the basics of self-concordance theory and interior point methods, including complexity results for LP, QP, and QP with quadratic constraint, semidefinite and conic programming. In the third part, the NR and Lagrangian transformation theories are considered and exterior point methods are described. Three important problems in finding equilibrium are considered in the fourth part. In the fifth and final part of the book, several important applications arising in economics, structural optimization, medicine, statistical learning theory, and more, are detailed. Numerical results, obtained by solving a number of real life and test problems, are also provided.