[PDF] Continuous Optimization eBook

Author : Niclas Andreasson
Publisher : Studentlitteratur AB
Page : 484 pages
File Size : 25,43 MB
Release : 2013-10-01
Category : Mathematics
ISBN : 9789144060774

GET BOOK

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 : V. Jeyakumar
Publisher : Springer Science & Business Media
Page : 277 pages
File Size : 36,49 MB
Release : 2007-10-23
Category : Mathematics
ISBN : 0387737170

GET BOOK

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.

Author : E. Spedicato
Publisher : Springer Science & Business Media
Page : 572 pages
File Size : 50,8 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 9400903693

GET BOOK

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 : Huyên Pham
Publisher : Springer Science & Business Media
Page : 243 pages
File Size : 12,96 MB
Release : 2009-05-28
Category : Mathematics
ISBN : 3540895000

GET BOOK

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.

Author : Mohit Tawarmalani
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 43,9 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 1475735324

GET BOOK

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.

Author : Niclas Andreasson
Publisher : Courier Dover Publications
Page : 515 pages
File Size : 16,61 MB
Release : 2020-01-15
Category : Mathematics
ISBN : 0486802876

GET BOOK

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 : Dimitri P. Bertsekas
Publisher : MIT Press
Page : 384 pages
File Size : 20,76 MB
Release : 1991
Category : Business & Economics
ISBN : 9780262023344

GET BOOK

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 : Fwu-Ranq Chang
Publisher : Cambridge University Press
Page : 346 pages
File Size : 16,21 MB
Release : 2004-04-26
Category : Business & Economics
ISBN : 1139452223

GET BOOK

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.

Author : V. Jeyakumar
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 17,61 MB
Release : 2005-08-10
Category : Business & Economics
ISBN : 9780387267692

GET BOOK

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.

Author : Giuseppe C. Calafiore
Publisher : Cambridge University Press
Page : 651 pages
File Size : 31,45 MB
Release : 2014-10-31
Category : Business & Economics
ISBN : 1107050871

GET BOOK

This accessible textbook demonstrates how to recognize, simplify, model and solve optimization problems - and apply these principles to new projects.