Introduction To Continuous Optimization

Author : Roman A. Polyak
Publisher : Springer Nature
Page : 552 pages
File Size : 43,5 Mb
Release : 2021-04-29
Category : Mathematics
ISBN : 9783030687137

Get Book

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 : Studentlitteratur AB
Page : 484 pages
File Size : 50,7 Mb
Release : 2013-10-01
Category : Mathematics
ISBN : 9144060777

Get Book

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 Andreasson,Anton Evgrafov,Michael Patriksson
Publisher : Courier Dover Publications
Page : 515 pages
File Size : 43,5 Mb
Release : 2020-01-15
Category : Mathematics
ISBN : 9780486802879

Get Book

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 Andréasson,Anton Evgrafov,Michael Patriksson
Publisher : Unknown
Page : 128 pages
File Size : 49,6 Mb
Release : 2016
Category : Electronic
ISBN : 9144115296

Get Book

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

Author : E. Spedicato
Publisher : Springer Science & Business Media
Page : 572 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400903692

Get Book

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 : Neculai Andrei
Publisher : Springer
Page : 506 pages
File Size : 46,6 Mb
Release : 2017-12-04
Category : Mathematics
ISBN : 9783319583563

Get Book

Continuous Nonlinear Optimization for Engineering Applications in GAMS Technology by Neculai Andrei Pdf

This book presents the theoretical details and computational performances of algorithms used for solving continuous nonlinear optimization applications imbedded in GAMS. Aimed toward scientists and graduate students who utilize optimization methods to model and solve problems in mathematical programming, operations research, business, engineering, and industry, this book enables readers with a background in nonlinear optimization and linear algebra to use GAMS technology to understand and utilize its important capabilities to optimize algorithms for modeling and solving complex, large-scale, continuous nonlinear optimization problems or applications. Beginning with an overview of constrained nonlinear optimization methods, this book moves on to illustrate key aspects of mathematical modeling through modeling technologies based on algebraically oriented modeling languages. Next, the main feature of GAMS, an algebraically oriented language that allows for high-level algebraic representation of mathematical optimization models, is introduced to model and solve continuous nonlinear optimization applications. More than 15 real nonlinear optimization applications in algebraic and GAMS representation are presented which are used to illustrate the performances of the algorithms described in this book. Theoretical and computational results, methods, and techniques effective for solving nonlinear optimization problems, are detailed through the algorithms MINOS, KNITRO, CONOPT, SNOPT and IPOPT which work in GAMS technology.

Author : Oliver Kramer
Publisher : Springer
Page : 94 pages
File Size : 52,9 Mb
Release : 2013-12-07
Category : Computers
ISBN : 3319034235

Get Book

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 : Edwin K. P. Chong,Stanislaw H. Żak
Publisher : John Wiley & Sons
Page : 646 pages
File Size : 51,7 Mb
Release : 2013-02-05
Category : Mathematics
ISBN : 9781118515150

Get Book

An Introduction to Optimization by Edwin K. P. Chong,Stanislaw H. Żak Pdf

Praise for the Third Edition ". . . guides and leads the reader through the learning path . . . [e]xamples are stated very clearly and the results are presented with attention to detail." —MAA Reviews Fully updated to reflect new developments in the field, the Fourth Edition of Introduction to Optimization fills the need for accessible treatment of optimization theory and methods with an emphasis on engineering design. Basic definitions and notations are provided in addition to the related fundamental background for linear algebra, geometry, and calculus. This new edition explores the essential topics of unconstrained optimization problems, linear programming problems, and nonlinear constrained optimization. The authors also present an optimization perspective on global search methods and include discussions on genetic algorithms, particle swarm optimization, and the simulated annealing algorithm. Featuring an elementary introduction to artificial neural networks, convex optimization, and multi-objective optimization, the Fourth Edition also offers: A new chapter on integer programming Expanded coverage of one-dimensional methods Updated and expanded sections on linear matrix inequalities Numerous new exercises at the end of each chapter MATLAB exercises and drill problems to reinforce the discussed theory and algorithms Numerous diagrams and figures that complement the written presentation of key concepts MATLAB M-files for implementation of the discussed theory and algorithms (available via the book's website) Introduction to Optimization, Fourth Edition is an ideal textbook for courses on optimization theory and methods. In addition, the book is a useful reference for professionals in mathematics, operations research, electrical engineering, economics, statistics, and business.

Author : Hubertus Th. Jongen,Klaus Meer,Eberhard Triesch
Publisher : Springer Science & Business Media
Page : 443 pages
File Size : 44,5 Mb
Release : 2007-05-08
Category : Mathematics
ISBN : 9781402080999

Get Book

Optimization Theory by Hubertus Th. Jongen,Klaus Meer,Eberhard Triesch Pdf

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.

Author : Wilhelm Forst,Dieter Hoffmann
Publisher : Springer Science & Business Media
Page : 420 pages
File Size : 40,5 Mb
Release : 2010-07-26
Category : Mathematics
ISBN : 9780387789767

Get Book

Optimization—Theory and Practice by Wilhelm Forst,Dieter Hoffmann Pdf

Optimization is a field important in its own right but is also integral to numerous applied sciences, including operations research, management science, economics, finance and all branches of mathematics-oriented engineering. Constrained optimization models are one of the most widely used mathematical models in operations research and management science. This book gives a modern and well-balanced presentation of the subject, focusing on theory but also including algorithims and examples from various real-world applications. Detailed examples and counter-examples are provided--as are exercises, solutions and helpful hints, and Matlab/Maple supplements.

Author : Dimitri P. Bertsekas
Publisher : MIT Press
Page : 384 pages
File Size : 54,5 Mb
Release : 1991
Category : Business & Economics
ISBN : 0262023342

Get Book

Linear Network Optimization by Dimitri P. Bertsekas Pdf

Linear Network Optimization presents a thorough treatment of classical approaches to network problems such as shortest path, max-flow, assignment, transportation, and minimum cost flow problems.

Author : Yurii Nesterov
Publisher : Springer
Page : 589 pages
File Size : 53,7 Mb
Release : 2018-11-19
Category : Mathematics
ISBN : 9783319915784

Get Book

Lectures on Convex Optimization by Yurii Nesterov Pdf

This book provides a comprehensive, modern introduction to convex optimization, a field that is becoming increasingly important in applied mathematics, economics and finance, engineering, and computer science, notably in data science and machine learning. Written by a leading expert in the field, this book includes recent advances in the algorithmic theory of convex optimization, naturally complementing the existing literature. It contains a unified and rigorous presentation of the acceleration techniques for minimization schemes of first- and second-order. It provides readers with a full treatment of the smoothing technique, which has tremendously extended the abilities of gradient-type methods. Several powerful approaches in structural optimization, including optimization in relative scale and polynomial-time interior-point methods, are also discussed in detail. Researchers in theoretical optimization as well as professionals working on optimization problems will find this book very useful. It presents many successful examples of how to develop very fast specialized minimization algorithms. Based on the author’s lectures, it can naturally serve as the basis for introductory and advanced courses in convex optimization for students in engineering, economics, computer science and mathematics.

Author : B. Guenin,J. Könemann,L. Tunçel
Publisher : Cambridge University Press
Page : 283 pages
File Size : 46,5 Mb
Release : 2014-07-31
Category : Business & Economics
ISBN : 9781107053441

Get Book

A Gentle Introduction to Optimization by B. Guenin,J. Könemann,L. Tunçel Pdf

Assuming only basic linear algebra, this textbook is the perfect starting point for undergraduate students from across the mathematical sciences.

Author : Jan Brinkhuis,Vladimir Tikhomirov
Publisher : Princeton University Press
Page : 683 pages
File Size : 47,5 Mb
Release : 2011-02-11
Category : Mathematics
ISBN : 9781400829361

Get Book

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 : Mykel J. Kochenderfer,Tim A. Wheeler
Publisher : MIT Press
Page : 521 pages
File Size : 45,6 Mb
Release : 2019-03-12
Category : Computers
ISBN : 9780262039420

Get Book

Algorithms for Optimization by Mykel J. Kochenderfer,Tim A. Wheeler Pdf

A comprehensive introduction to optimization with a focus on practical algorithms for the design of engineering systems. This book offers a comprehensive introduction to optimization with a focus on practical algorithms. The book approaches optimization from an engineering perspective, where the objective is to design a system that optimizes a set of metrics subject to constraints. Readers will learn about computational approaches for a range of challenges, including searching high-dimensional spaces, handling problems where there are multiple competing objectives, and accommodating uncertainty in the metrics. Figures, examples, and exercises convey the intuition behind the mathematical approaches. The text provides concrete implementations in the Julia programming language. Topics covered include derivatives and their generalization to multiple dimensions; local descent and first- and second-order methods that inform local descent; stochastic methods, which introduce randomness into the optimization process; linear constrained optimization, when both the objective function and the constraints are linear; surrogate models, probabilistic surrogate models, and using probabilistic surrogate models to guide optimization; optimization under uncertainty; uncertainty propagation; expression optimization; and multidisciplinary design optimization. Appendixes offer an introduction to the Julia language, test functions for evaluating algorithm performance, and mathematical concepts used in the derivation and analysis of the optimization methods discussed in the text. The book can be used by advanced undergraduates and graduate students in mathematics, statistics, computer science, any engineering field, (including electrical engineering and aerospace engineering), and operations research, and as a reference for professionals.