Continuous Optimization

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Anintroduction to Continuous Optimization / Second Edition

Niclas Andreasson,Anton Evgrafov,Michael Patriksson
Anintroduction to Continuous Optimization Second Edition Book PDF

Author : Niclas Andreasson,Anton Evgrafov,Michael Patriksson
Publisher : Studentlitteratur AB
Page : 484 pages
File Size : 45,7 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.

Algorithms for Continuous Optimization

E. Spedicato
Algorithms for Continuous Optimization Book PDF

Author : E. Spedicato
Publisher : Springer Science & Business Media
Page : 572 pages
File Size : 40,8 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.

Nonsmooth Vector Functions and Continuous Optimization

V. Jeyakumar,Dinh The Luc
Nonsmooth Vector Functions and Continuous Optimization Book PDF

Author : V. Jeyakumar,Dinh The Luc
Publisher : Springer Science & Business Media
Page : 270 pages
File Size : 41,6 Mb
Release : 2007-10-23
Category : Mathematics
ISBN : 9780387737171

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Nonsmooth Vector Functions and Continuous Optimization by V. Jeyakumar,Dinh The Luc Pdf

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.

Continuous-time Stochastic Control and Optimization with Financial Applications

Huyên Pham
Continuous time Stochastic Control and Optimization with Financial Applications Book PDF

Author : Huyên Pham
Publisher : Springer Science & Business Media
Page : 243 pages
File Size : 54,5 Mb
Release : 2009-05-28
Category : Mathematics
ISBN : 9783540895008

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Continuous-time Stochastic Control and Optimization with Financial Applications by Huyên Pham Pdf

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.

Continuous Nonlinear Optimization for Engineering Applications in GAMS Technology

Neculai Andrei
Continuous Nonlinear Optimization for Engineering Applications in GAMS Technology Book PDF

Author : Neculai Andrei
Publisher : Springer
Page : 506 pages
File Size : 53,6 Mb
Release : 2017-12-04
Category : Mathematics
ISBN : 9783319583563

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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.

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

Mohit Tawarmalani,Nikolaos V. Sahinidis
Convexification and Global Optimization in Continuous and Mixed Integer Nonlinear Programming Book PDF

Author : Mohit Tawarmalani,Nikolaos V. Sahinidis
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 53,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475735321

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Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming by Mohit Tawarmalani,Nikolaos V. Sahinidis Pdf

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

Niclas Andreasson,Anton Evgrafov,Michael Patriksson
An Introduction to Continuous Optimization Book PDF

Author : Niclas Andreasson,Anton Evgrafov,Michael Patriksson
Publisher : Courier Dover Publications
Page : 515 pages
File Size : 54,7 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.

Global Optimization in Action

János D. Pintér
Global Optimization in Action Book PDF

Author : János D. Pintér
Publisher : Springer Science & Business Media
Page : 481 pages
File Size : 52,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475725025

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Global Optimization in Action by János D. Pintér Pdf

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

Fwu-Ranq Chang
Stochastic Optimization in Continuous Time Book PDF

Author : Fwu-Ranq Chang
Publisher : Cambridge University Press
Page : 346 pages
File Size : 42,5 Mb
Release : 2004-04-26
Category : Business & Economics
ISBN : 9781139452229

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Stochastic Optimization in Continuous Time by Fwu-Ranq Chang Pdf

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.

Computational Collective Intelligence. Technologies and Applications

Costin Badica,Ngoc Thanh Nguyen,Marius Brezovan
Computational Collective Intelligence Technologies and Applications Book PDF

Author : Costin Badica,Ngoc Thanh Nguyen,Marius Brezovan
Publisher : Springer
Page : 740 pages
File Size : 46,8 Mb
Release : 2013-09-03
Category : Computers
ISBN : 9783642404955

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Computational Collective Intelligence. Technologies and Applications by Costin Badica,Ngoc Thanh Nguyen,Marius Brezovan Pdf

This book constitutes the thoroughly refereed conference proceedings of the 5th International Conference on Computational Collective Intelligence, ICCCI 2013, held in Craiova, Romania, in September 2013. The 72 revised full papers presented were carefully selected from numerous submissions. Conference papers are organized in 16 technical sessions, covering the following topics: intelligent e-learning, classification and clustering methods, web intelligence and interaction, agents and multi-agent systems, social networks, intelligent knowledge management, language processing systems, modeling and optimization techniques, evolutionary computation, intelligent and group decision making, swarm intelligence, data mining techniques and applications, cooperative problem solving, collective intelligence for text mining and innovation, collective intelligence for social understanding and mining, and soft methods in collective intelligence.

Continuous Optimization

V. Jeyakumar,Alexander M. Rubinov
Continuous Optimization Book PDF

Author : V. Jeyakumar,Alexander M. Rubinov
Publisher : Springer Science & Business Media
Page : 454 pages
File Size : 53,5 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.

Handbook of Memetic Algorithms

Ferrante Neri,Carlos Cotta,Pablo Moscato
Handbook of Memetic Algorithms Book PDF

Author : Ferrante Neri,Carlos Cotta,Pablo Moscato
Publisher : Springer
Page : 370 pages
File Size : 55,6 Mb
Release : 2011-10-29
Category : Technology & Engineering
ISBN : 9783642232473

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Handbook of Memetic Algorithms by Ferrante Neri,Carlos Cotta,Pablo Moscato Pdf

Memetic Algorithms (MAs) are computational intelligence structures combining multiple and various operators in order to address optimization problems. The combination and interaction amongst operators evolves and promotes the diffusion of the most successful units and generates an algorithmic behavior which can handle complex objective functions and hard fitness landscapes. “Handbook of Memetic Algorithms” organizes, in a structured way, all the the most important results in the field of MAs since their earliest definition until now. A broad review including various algorithmic solutions as well as successful applications is included in this book. Each class of optimization problems, such as constrained optimization, multi-objective optimization, continuous vs combinatorial problems, uncertainties, are analysed separately and, for each problem, memetic recipes for tackling the difficulties are given with some successful examples. Although this book contains chapters written by multiple authors, a great attention has been given by the editors to make it a compact and smooth work which covers all the main areas of computational intelligence optimization. It is not only a necessary read for researchers working in the research area, but also a useful handbook for practitioners and engineers who need to address real-world optimization problems. In addition, the book structure makes it an interesting work also for graduate students and researchers is related fields of mathematics and computer science.

Numerical Optimization

Jorge Nocedal,Stephen Wright
Numerical Optimization Book PDF

Author : Jorge Nocedal,Stephen Wright
Publisher : Springer Science & Business Media
Page : 664 pages
File Size : 40,5 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.

A Brief Introduction to Continuous Evolutionary Optimization

Oliver Kramer
A Brief Introduction to Continuous Evolutionary Optimization Book PDF

Author : Oliver Kramer
Publisher : Springer
Page : 94 pages
File Size : 52,7 Mb
Release : 2013-12-07
Category : Computers
ISBN : 3319034235

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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.

Mathematical Models and Algorithms for Power System Optimization

Mingtian Fan,Zuping Zhang,Chengmin Wang
Mathematical Models and Algorithms for Power System Optimization Book PDF

Author : Mingtian Fan,Zuping Zhang,Chengmin Wang
Publisher : Academic Press
Page : 450 pages
File Size : 51,9 Mb
Release : 2019-08-23
Category : Technology & Engineering
ISBN : 9780128132319

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Mathematical Models and Algorithms for Power System Optimization by Mingtian Fan,Zuping Zhang,Chengmin Wang Pdf

Mathematical Models and Algorithms for Power System Optimization helps readers build a thorough understanding of new technologies and world-class practices developed by the State Grid Corporation of China, the organization responsible for the world's largest power distribution network. This reference covers three areas: power operation planning, electric grid investment and operational planning and power system control. It introduces economic dispatching, generator maintenance scheduling, power flow, optimal load flow, reactive power planning, load frequency control and transient stability, using mathematic models including optimization, dynamic, differential and difference equations. Provides insights on the development of new mathematical models of power system optimization Analyzes power systems comprehensively to create novel mathematic models and algorithms for issues related to the planning operation of power systems Includes research on the optimization of power systems and related practical research projects carried out since 1981