Continuous Optimization

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Anintroduction to Continuous Optimization / Second Edition

Author : Niclas Andreasson
Publisher : Studentlitteratur AB
ISBN 13 : 9789144060774
Total Pages : 484 pages
Book Rating : 4.0/5 (67 download)

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Book Synopsis Anintroduction to Continuous Optimization / Second Edition by : Niclas Andreasson

Download or read book Anintroduction to Continuous Optimization / Second Edition written by Niclas Andreasson and published by Studentlitteratur AB. This book was released on 2013-10-01 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algorithms for Continuous Optimization

Author : E. Spedicato
Publisher : Springer Science & Business Media
ISBN 13 : 9400903693
Total Pages : 572 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Algorithms for Continuous Optimization by : E. Spedicato

Download or read book Algorithms for Continuous Optimization written by E. Spedicato and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Continuous Optimization

Author : V. Jeyakumar
Publisher : Springer Science & Business Media
ISBN 13 : 9780387267692
Total Pages : 476 pages
Book Rating : 4.2/5 (676 download)

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Book Synopsis Continuous Optimization by : V. Jeyakumar

Download or read book Continuous Optimization written by V. Jeyakumar and published by Springer Science & Business Media. This book was released on 2005-08-10 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The search for the best possible performance is inherent in human nature. Individuals, enterprises and governments all seek optimal—that is, the best—possible solutions of problems that they meet. Evidently, continuous optimization plays an increasingly significant role in everyday management and technical decisions in science, engineering and commerce. The collection of 16 refereed papers in this book covers a diverse number of topics and provides a good picture of recent research in continuous optimization. The first part of the book presents substantive survey articles in a number of important topic areas of continuous optimization. Most of the papers in the second part present results on the theoretical aspects as well as numerical methods of continuous optimization. The papers in the third part are mainly concerned with applications of continuous optimization. Hence, the book will be an additional valuable source of information to faculty, students, and researchers who use continuous optimization to model and solve problems. Audience This book is intended for researchers in mathematical programming, optimization and operations research; engineers in various fields; and graduate students in applied mathematics, engineering and operations research.

Nonsmooth Vector Functions and Continuous Optimization

Author : V. Jeyakumar
Publisher : Springer Science & Business Media
ISBN 13 : 0387737170
Total Pages : 277 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Nonsmooth Vector Functions and Continuous Optimization by : V. Jeyakumar

Download or read book Nonsmooth Vector Functions and Continuous Optimization written by V. Jeyakumar and published by Springer Science & Business Media. This book was released on 2007-10-23 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on the study of nonsmooth vector functions, this book presents a comprehensive account of the calculus of generalized Jacobian matrices and their applications to continuous nonsmooth optimization problems, as well as variational inequalities in finite dimensions. The treatment is motivated by a desire to expose an elementary approach to nonsmooth calculus, using a set of matrices to replace the nonexistent Jacobian matrix of a continuous vector function.

Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming

Author : Mohit Tawarmalani
Publisher : Springer Science & Business Media
ISBN 13 : 1475735324
Total Pages : 492 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming by : Mohit Tawarmalani

Download or read book Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming written by Mohit Tawarmalani and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest in constrained optimization originated with the simple linear pro gramming model since it was practical and perhaps the only computationally tractable model at the time. Constrained linear optimization models were soon adopted in numerous application areas and are perhaps the most widely used mathematical models in operations research and management science at the time of this writing. Modelers have, however, found the assumption of linearity to be overly restrictive in expressing the real-world phenomena and problems in economics, finance, business, communication, engineering design, computational biology, and other areas that frequently demand the use of nonlinear expressions and discrete variables in optimization models. Both of these extensions of the linear programming model are NP-hard, thus representing very challenging problems. On the brighter side, recent advances in algorithmic and computing technology make it possible to re visit these problems with the hope of solving practically relevant problems in reasonable amounts of computational time. Initial attempts at solving nonlinear programs concentrated on the de velopment of local optimization methods guaranteeing globality under the assumption of convexity. On the other hand, the integer programming liter ature has concentrated on the development of methods that ensure global optima. The aim of this book is to marry the advancements in solving nonlinear and integer programming models and to develop new results in the more general framework of mixed-integer nonlinear programs (MINLPs) with the goal of devising practically efficient global optimization algorithms for MINLPs.

An Introduction to Continuous Optimization

Author : Niclas Andreasson
Publisher : Courier Dover Publications
ISBN 13 : 0486802876
Total Pages : 515 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis An Introduction to Continuous Optimization by : Niclas Andreasson

Download or read book An Introduction to Continuous Optimization written by Niclas Andreasson and published by Courier Dover Publications. This book was released on 2020-01-15 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Continuous-time Stochastic Control and Optimization with Financial Applications

Author : Huyên Pham
Publisher : Springer Science & Business Media
ISBN 13 : 3540895000
Total Pages : 243 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Continuous-time Stochastic Control and Optimization with Financial Applications by : Huyên Pham

Download or read book Continuous-time Stochastic Control and Optimization with Financial Applications written by Huyên Pham and published by Springer Science & Business Media. This book was released on 2009-05-28 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control. This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc. This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.

Linear Network Optimization

Author : Dimitri P. Bertsekas
Publisher : MIT Press
ISBN 13 : 9780262023344
Total Pages : 384 pages
Book Rating : 4.0/5 (233 download)

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Book Synopsis Linear Network Optimization by : Dimitri P. Bertsekas

Download or read book Linear Network Optimization written by Dimitri P. Bertsekas and published by MIT Press. This book was released on 1991 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Global Optimization in Action

Author : János D. Pintér
Publisher : Springer Science & Business Media
ISBN 13 : 1475725027
Total Pages : 481 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Global Optimization in Action by : János D. Pintér

Download or read book Global Optimization in Action written by János D. Pintér and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: In science, engineering and economics, decision problems are frequently modelled by optimizing the value of a (primary) objective function under stated feasibility constraints. In many cases of practical relevance, the optimization problem structure does not warrant the global optimality of local solutions; hence, it is natural to search for the globally best solution(s). Global Optimization in Action provides a comprehensive discussion of adaptive partition strategies to solve global optimization problems under very general structural requirements. A unified approach to numerous known algorithms makes possible straightforward generalizations and extensions, leading to efficient computer-based implementations. A considerable part of the book is devoted to applications, including some generic problems from numerical analysis, and several case studies in environmental systems analysis and management. The book is essentially self-contained and is based on the author's research, in cooperation (on applications) with a number of colleagues. Audience: Professors, students, researchers and other professionals in the fields of operations research, management science, industrial and applied mathematics, computer science, engineering, economics and the environmental sciences.

Stochastic Optimization in Continuous Time

Author : Fwu-Ranq Chang
Publisher : Cambridge University Press
ISBN 13 : 1139452223
Total Pages : 346 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Stochastic Optimization in Continuous Time by : Fwu-Ranq Chang

Download or read book Stochastic Optimization in Continuous Time written by Fwu-Ranq Chang and published by Cambridge University Press. This book was released on 2004-04-26 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 2004, this is a rigorous but user-friendly book on the application of stochastic control theory to economics. A distinctive feature of the book is that mathematical concepts are introduced in a language and terminology familiar to graduate students of economics. The standard topics of many mathematics, economics and finance books are illustrated with real examples documented in the economic literature. Moreover, the book emphasises the dos and don'ts of stochastic calculus, cautioning the reader that certain results and intuitions cherished by many economists do not extend to stochastic models. A special chapter (Chapter 5) is devoted to exploring various methods of finding a closed-form representation of the value function of a stochastic control problem, which is essential for ascertaining the optimal policy functions. The book also includes many practice exercises for the reader. Notes and suggested readings are provided at the end of each chapter for more references and possible extensions.

Numerical Optimization

Author : Jorge Nocedal
Publisher : Springer Science & Business Media
ISBN 13 : 0387400656
Total Pages : 686 pages
Book Rating : 4.3/5 (874 download)

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Book Synopsis Numerical Optimization by : Jorge Nocedal

Download or read book Numerical Optimization written by Jorge Nocedal and published by Springer Science & Business Media. This book was released on 2006-12-11 with total page 686 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algorithms for Convex Optimization

Author : Nisheeth K. Vishnoi
Publisher : Cambridge University Press
ISBN 13 : 1108633994
Total Pages : 314 pages
Book Rating : 4.1/5 (86 download)

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Book Synopsis Algorithms for Convex Optimization by : Nisheeth K. Vishnoi

Download or read book Algorithms for Convex Optimization written by Nisheeth K. Vishnoi and published by Cambridge University Press. This book was released on 2021-10-07 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last few years, Algorithms for Convex Optimization have revolutionized algorithm design, both for discrete and continuous optimization problems. For problems like maximum flow, maximum matching, and submodular function minimization, the fastest algorithms involve essential methods such as gradient descent, mirror descent, interior point methods, and ellipsoid methods. The goal of this self-contained book is to enable researchers and professionals in computer science, data science, and machine learning to gain an in-depth understanding of these algorithms. The text emphasizes how to derive key algorithms for convex optimization from first principles and how to establish precise running time bounds. This modern text explains the success of these algorithms in problems of discrete optimization, as well as how these methods have significantly pushed the state of the art of convex optimization itself.

Bayesian Heuristic Approach to Discrete and Global Optimization

Author : Jonas Mockus
Publisher : Springer Science & Business Media
ISBN 13 : 1475726279
Total Pages : 394 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Bayesian Heuristic Approach to Discrete and Global Optimization by : Jonas Mockus

Download or read book Bayesian Heuristic Approach to Discrete and Global Optimization written by Jonas Mockus and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian decision theory is known to provide an effective framework for the practical solution of discrete and nonconvex optimization problems. This book is the first to demonstrate that this framework is also well suited for the exploitation of heuristic methods in the solution of such problems, especially those of large scale for which exact optimization approaches can be prohibitively costly. The book covers all aspects ranging from the formal presentation of the Bayesian Approach, to its extension to the Bayesian Heuristic Strategy, and its utilization within the informal, interactive Dynamic Visualization strategy. The developed framework is applied in forecasting, in neural network optimization, and in a large number of discrete and continuous optimization problems. Specific application areas which are discussed include scheduling and visualization problems in chemical engineering, manufacturing process control, and epidemiology. Computational results and comparisons with a broad range of test examples are presented. The software required for implementation of the Bayesian Heuristic Approach is included. Although some knowledge of mathematical statistics is necessary in order to fathom the theoretical aspects of the development, no specialized mathematical knowledge is required to understand the application of the approach or to utilize the software which is provided. Audience: The book is of interest to both researchers in operations research, systems engineering, and optimization methods, as well as applications specialists concerned with the solution of large scale discrete and/or nonconvex optimization problems in a broad range of engineering and technological fields. It may be used as supplementary material for graduate level courses.

Network Optimization

Author : Panos M. Pardalos
Publisher : Springer Science & Business Media
ISBN 13 : 3642591795
Total Pages : 495 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Network Optimization by : Panos M. Pardalos

Download or read book Network Optimization written by Panos M. Pardalos and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: Network optimization is important in the modeling of problems and processes from such fields as engineering, computer science, operations research, transportation, telecommunication, decision support systems, manufacturing, and airline scheduling. Recent advances in data structures, computer technology, and algorithm development have made it possible to solve classes of network optimization problems that until recently were intractable. The refereed papers in this volume reflect the interdisciplinary efforts of a large group of scientists from academia and industry to model and solve complicated large-scale network optimization problems.

A Brief Introduction to Continuous Evolutionary Optimization

Author : Oliver Kramer
Publisher : Springer
ISBN 13 : 9783319034232
Total Pages : 94 pages
Book Rating : 4.0/5 (342 download)

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Book Synopsis A Brief Introduction to Continuous Evolutionary Optimization by : Oliver Kramer

Download or read book A Brief Introduction to Continuous Evolutionary Optimization written by Oliver Kramer and published by Springer. This book was released on 2013-12-07 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Perturbation Analysis of Optimization Problems

Author : J.Frederic Bonnans
Publisher : Springer Science & Business Media
ISBN 13 : 1461213940
Total Pages : 618 pages
Book Rating : 4.4/5 (612 download)

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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.

Introduction to Continuous Optimization

Author : Roman A. Polyak
Publisher : Springer Nature
ISBN 13 : 3030687139
Total Pages : 552 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Introduction to Continuous Optimization by : Roman A. Polyak

Download or read book Introduction to Continuous Optimization written by Roman A. Polyak and published by Springer Nature. This book was released on 2021-04-29 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.