Anintroduction To Continuous Optimization Second Edition

Author : Roman A. Polyak
Publisher : Springer Nature
Page : 552 pages
File Size : 53,9 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.

Author : Niclas Andreasson,Anton Evgrafov,Michael Patriksson
Publisher : Courier Dover Publications
Page : 515 pages
File Size : 50,5 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 : Niclas Andreasson,Anton Evgrafov,Michael Patriksson
Publisher : Studentlitteratur AB
Page : 484 pages
File Size : 40,7 Mb
Release : 2013-10-01
Category : Mathematics
ISBN : 9144060777

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Anintroduction to Continuous Optimization / Second Edition by Niclas Andreasson,Anton Evgrafov,Michael Patriksson Pdf

Optimisation, or mathematical programming, is a fundamental subject within decision science and operations research, in which mathematical decision models are constructed, analysed, and solved. The books focus lies on providing a basis for the analysis of optimisation models and of candidate optimal solutions for continuous optimisation models. The main part of the mathematical material therefore concerns the analysis and linear algebra that underlie the workings of convexity and duality, and necessary/sufficient local/global optimality conditions for continuous optimisation problems. Natural algorithms are then developed from these optimality conditions, and their most important convergence characteristics are analysed. The book answers many more questions of the form Why? and Why not? than How?. We use only elementary mathematics in the development of the book, yet are rigorous throughout. The book provides lecture, exercise and reading material for a first course on continuous optimisation and mathematical programming, geared towards third-year students, and has already been used as such for nearly ten years. The preface to the second edition describes the main changes made since the first, 2005, edition. The book can be used in mathematical optimisation courses at any mathematics, engineering, economics, and business schools. It is a perfect starting book for anyone who wishes to develop his/her understanding of the subject of optimisation, before actually applying it.

Author : Niclas Andréasson,Anton Evgrafov,Michael Patriksson
Publisher : Unknown
Page : 128 pages
File Size : 45,7 Mb
Release : 2016
Category : Electronic
ISBN : 9144115296

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

Author : V. Jeyakumar,Alexander M. Rubinov
Publisher : Springer Science & Business Media
Page : 454 pages
File Size : 42,9 Mb
Release : 2006-03-09
Category : Mathematics
ISBN : 9780387267715

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Continuous Optimization by V. Jeyakumar,Alexander M. Rubinov Pdf

Continuous optimization is the study of problems in which we wish to opti mize (either maximize or minimize) a continuous function (usually of several variables) often subject to a collection of restrictions on these variables. It has its foundation in the development of calculus by Newton and Leibniz in the 17*^ century. Nowadys, continuous optimization problems are widespread in the mathematical modelling of real world systems for a very broad range of applications. Solution methods for large multivariable constrained continuous optimiza tion problems using computers began with the work of Dantzig in the late 1940s on the simplex method for linear programming problems. Recent re search in continuous optimization has produced a variety of theoretical devel opments, solution methods and new areas of applications. It is impossible to give a full account of the current trends and modern applications of contin uous optimization. It is our intention to present a number of topics in order to show the spectrum of current research activities and the development of numerical methods and applications.

Author : Jonathan M. Borwein,Adrian S. Lewis
Publisher : Springer Science & Business Media
Page : 281 pages
File Size : 47,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475798593

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Convex Analysis and Nonlinear Optimization by Jonathan M. Borwein,Adrian S. Lewis Pdf

This book provides a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. It can serve as a teaching text, at roughly the level of first year graduate students, since the main body of the text is self-contained, with each section rounded off by an often extensive set of optional exercises. The new edition adds material on semismooth optimization, as well as several new proofs that will make this book even more self-contained.

Author : Johannes Jahn
Publisher : Springer Nature
Page : 325 pages
File Size : 55,5 Mb
Release : 2020-07-02
Category : Business & Economics
ISBN : 9783030427603

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Introduction to the Theory of Nonlinear Optimization by Johannes Jahn Pdf

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.

Author : Jan Brinkhuis,Vladimir Tikhomirov
Publisher : Princeton University Press
Page : 683 pages
File Size : 51,9 Mb
Release : 2011-02-11
Category : Mathematics
ISBN : 9781400829361

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Optimization by Jan Brinkhuis,Vladimir Tikhomirov Pdf

This self-contained textbook is an informal introduction to optimization through the use of numerous illustrations and applications. The focus is on analytically solving optimization problems with a finite number of continuous variables. In addition, the authors provide introductions to classical and modern numerical methods of optimization and to dynamic optimization. The book's overarching point is that most problems may be solved by the direct application of the theorems of Fermat, Lagrange, and Weierstrass. The authors show how the intuition for each of the theoretical results can be supported by simple geometric figures. They include numerous applications through the use of varied classical and practical problems. Even experts may find some of these applications truly surprising. A basic mathematical knowledge is sufficient to understand the topics covered in this book. More advanced readers, even experts, will be surprised to see how all main results can be grounded on the Fermat-Lagrange theorem. The book can be used for courses on continuous optimization, from introductory to advanced, for any field for which optimization is relevant.

Author : Matthias Beck,Sinai Robins
Publisher : Springer Science & Business Media
Page : 227 pages
File Size : 48,7 Mb
Release : 2007-11-27
Category : Mathematics
ISBN : 9780387461120

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Computing the Continuous Discretely by Matthias Beck,Sinai Robins Pdf

This textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory. We encounter here a friendly invitation to the field of "counting integer points in polytopes", and its various connections to elementary finite Fourier analysis, generating functions, the Frobenius coin-exchange problem, solid angles, magic squares, Dedekind sums, computational geometry, and more. With 250 exercises and open problems, the reader feels like an active participant.

Author : Horst A. Eiselt,Giorgio Pederzoli,Carl-Louis Sandblom
Publisher : Unknown
Page : 730 pages
File Size : 42,6 Mb
Release : 1987
Category : Programming (Mathematics)
ISBN : 0899250165

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Continuous Optimization Models by Horst A. Eiselt,Giorgio Pederzoli,Carl-Louis Sandblom Pdf

Author : E. Spedicato
Publisher : Springer Science & Business Media
Page : 572 pages
File Size : 46,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400903692

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Algorithms for Continuous Optimization by E. Spedicato Pdf

The NATO Advanced Study Institute on "Algorithms for continuous optimiza tion: the state of the art" was held September 5-18, 1993, at II Ciocco, Barga, Italy. It was attended by 75 students (among them many well known specialists in optimiza tion) from the following countries: Belgium, Brasil, Canada, China, Czech Republic, France, Germany, Greece, Hungary, Italy, Poland, Portugal, Rumania, Spain, Turkey, UK, USA, Venezuela. The lectures were given by 17 well known specialists in the field, from Brasil, China, Germany, Italy, Portugal, Russia, Sweden, UK, USA. Solving continuous optimization problems is a fundamental task in computational mathematics for applications in areas of engineering, economics, chemistry, biology and so on. Most real problems are nonlinear and can be of quite large size. Devel oping efficient algorithms for continuous optimization has been an important field of research in the last 30 years, with much additional impetus provided in the last decade by the availability of very fast and parallel computers. Techniques, like the simplex method, that were already considered fully developed thirty years ago have been thoroughly revised and enormously improved. The aim of this ASI was to present the state of the art in this field. While not all important aspects could be covered in the fifty hours of lectures (for instance multiob jective optimization had to be skipped), we believe that most important topics were presented, many of them by scientists who greatly contributed to their development.

Author : Jorge Nocedal,Stephen Wright
Publisher : Springer Science & Business Media
Page : 664 pages
File Size : 44,9 Mb
Release : 2006-12-11
Category : Mathematics
ISBN : 9780387400655

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Numerical Optimization by Jorge Nocedal,Stephen Wright Pdf

Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.

Author : Oliver Kramer
Publisher : Springer Science & Business Media
Page : 94 pages
File Size : 48,5 Mb
Release : 2013-12-04
Category : Technology & Engineering
ISBN : 9783319034225

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A Brief Introduction to Continuous Evolutionary Optimization by Oliver Kramer Pdf

Practical optimization problems are often hard to solve, in particular when they are black boxes and no further information about the problem is available except via function evaluations. This work introduces a collection of heuristics and algorithms for black box optimization with evolutionary algorithms in continuous solution spaces. The book gives an introduction to evolution strategies and parameter control. Heuristic extensions are presented that allow optimization in constrained, multimodal and multi-objective solution spaces. An adaptive penalty function is introduced for constrained optimization. Meta-models reduce the number of fitness and constraint function calls in expensive optimization problems. The hybridization of evolution strategies with local search allows fast optimization in solution spaces with many local optima. A selection operator based on reference lines in objective space is introduced to optimize multiple conflictive objectives. Evolutionary search is employed for learning kernel parameters of the Nadaraya-Watson estimator and a swarm-based iterative approach is presented for optimizing latent points in dimensionality reduction problems. Experiments on typical benchmark problems as well as numerous figures and diagrams illustrate the behavior of the introduced concepts and methods.

Author : Mariano Martín Martín
Publisher : CRC Press
Page : 786 pages
File Size : 51,5 Mb
Release : 2019-06-06
Category : Computers
ISBN : 9780429835438

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Introduction to Software for Chemical Engineers, Second Edition by Mariano Martín Martín Pdf

The field of Chemical Engineering and its link to computer science is in constant evolution and new engineers have a variety of tools at their disposal to tackle their everyday problems. Introduction to Software for Chemical Engineers, Second Edition provides a quick guide to the use of various computer packages for chemical engineering applications. It covers a range of software applications from Excel and general mathematical packages such as MATLAB and MathCAD to process simulators, CHEMCAD and ASPEN, equation-based modeling languages, gProms, optimization software such as GAMS and AIMS, and specialized software like CFD or DEM codes. The different packages are introduced and applied to solve typical problems in fluid mechanics, heat and mass transfer, mass and energy balances, unit operations, reactor engineering, process and equipment design and control. This new edition offers a wider view of packages including open source software such as R, Python and Julia. It also includes complete examples in ASPEN Plus, adds ANSYS Fluent to CFD codes, Lingo to the optimization packages, and discusses Engineering Equation Solver. It offers a global idea of the capabilities of the software used in the chemical engineering field and provides examples for solving real-world problems. Written by leading experts, this book is a must-have reference for chemical engineers looking to grow in their careers through the use of new and improving computer software. Its user-friendly approach to simulation and optimization as well as its example-based presentation of the software, makes it a perfect teaching tool for both undergraduate and master levels.

Author : P. Adby
Publisher : Springer Science & Business Media
Page : 214 pages
File Size : 42,8 Mb
Release : 2013-03-09
Category : Science
ISBN : 9789400957053

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Introduction to Optimization Methods by P. Adby Pdf

During the last decade the techniques of non-linear optim ization have emerged as an important subject for study and research. The increasingly widespread application of optim ization has been stimulated by the availability of digital computers, and the necessity of using them in the investigation of large systems. This book is an introduction to non-linear methods of optimization and is suitable for undergraduate and post graduate courses in mathematics, the physical and social sciences, and engineering. The first half of the book covers the basic optimization techniques including linear search methods, steepest descent, least squares, and the Newton-Raphson method. These are described in detail, with worked numerical examples, since they form the basis from which advanced methods are derived. Since 1965 advanced methods of unconstrained and constrained optimization have been developed to utilise the computational power of the digital computer. The second half of the book describes fully important algorithms in current use such as variable metric methods for unconstrained problems and penalty function methods for constrained problems. Recent work, much of which has not yet been widely applied, is reviewed and compared with currently popular techniques under a few generic main headings. vi PREFACE Chapter I describes the optimization problem in mathemat ical form and defines the terminology used in the remainder of the book. Chapter 2 is concerned with single variable optimization. The main algorithms of both search and approximation methods are developed in detail since they are an essential part of many multi-variable methods.