Optimal Quadratic Programming Algorithms
Optimal Quadratic Programming Algorithms

Author: Zdenek Dostál

Publisher: Springer Science & Business Media

Published: 2009-04-03

Total Pages: 293

ISBN-13: 0387848061

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Quadratic programming (QP) is one advanced mathematical technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. This book presents recently developed algorithms for solving large QP problems and focuses on algorithms which are, in a sense optimal, i.e., they can solve important classes of problems at a cost proportional to the number of unknowns. For each algorithm presented, the book details its classical predecessor, describes its drawbacks, introduces modifications that improve its performance, and demonstrates these improvements through numerical experiments. This self-contained monograph can serve as an introductory text on quadratic programming for graduate students and researchers. Additionally, since the solution of many nonlinear problems can be reduced to the solution of a sequence of QP problems, it can also be used as a convenient introduction to nonlinear programming.

Computational Mathematical Programming
Computational Mathematical Programming

Author: Klaus Schittkowski

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 455

ISBN-13: 3642824501

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This book contains the written versions of main lectures presented at the Advanced Study Institute (ASI) on Computational Mathematical Programming, which was held in Bad Windsheim, Germany F. R., from July 23 to August 2, 1984, under the sponsorship of NATO. The ASI was organized by the Committee on Algorithms (COAL) of the Mathematical Programming Society. Co-directors were Karla Hoffmann (National Bureau of Standards, Washington, U.S.A.) and Jan Teigen (Rabobank Nederland, Zeist, The Netherlands). Ninety participants coming from about 20 different countries attended the ASI and contributed their efforts to achieve a highly interesting and stimulating meeting. Since 1947 when the first linear programming technique was developed, the importance of optimization models and their mathematical solution methods has steadily increased, and now plays a leading role in applied research areas. The basic idea of optimization theory is to minimize (or maximize) a function of several variables subject to certain restrictions. This general mathematical concept covers a broad class of possible practical applications arising in mechanical, electrical, or chemical engineering, physics, economics, medicine, biology, etc. There are both industrial applications (e.g. design of mechanical structures, production plans) and applications in the natural, engineering, and social sciences (e.g. chemical equilibrium problems, christollography problems).

Introduction to Optimum Design
Introduction to Optimum Design

Author: Jasbir Singh Arora

Publisher: Academic Press

Published: 2011-08-12

Total Pages: 897

ISBN-13: 012381376X

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Introduction to Optimum Design, Third Edition describes an organized approach to engineering design optimization in a rigorous yet simplified manner. It illustrates various concepts and procedures with simple examples and demonstrates their applicability to engineering design problems. Formulation of a design problem as an optimization problem is emphasized and illustrated throughout the text. Excel and MATLAB® are featured as learning and teaching aids. - Basic concepts of optimality conditions and numerical methods are described with simple and practical examples, making the material highly teachable and learnable - Includes applications of optimization methods for structural, mechanical, aerospace, and industrial engineering problems - Introduction to MATLAB Optimization Toolbox - Practical design examples introduce students to the use of optimization methods early in the book - New example problems throughout the text are enhanced with detailed illustrations - Optimum design with Excel Solver has been expanded into a full chapter - New chapter on several advanced optimum design topics serves the needs of instructors who teach more advanced courses

Numerical Optimization
Numerical Optimization

Author: Jorge Nocedal

Publisher: Springer Science & Business Media

Published: 2006-12-11

Total Pages: 686

ISBN-13: 0387400656

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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.

Numerical Methods for Unconstrained Optimization and Nonlinear Equations
Numerical Methods for Unconstrained Optimization and Nonlinear Equations

Author: J. E. Dennis, Jr.

Publisher: SIAM

Published: 1996-12-01

Total Pages: 394

ISBN-13: 9781611971200

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This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or "quasi-Newton" methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems. The level of presentation is consistent throughout, with a good mix of examples and theory, making it a valuable text at both the graduate and undergraduate level. It has been praised as excellent for courses with approximately the same name as the book title and would also be useful as a supplemental text for a nonlinear programming or a numerical analysis course. Many exercises are provided to illustrate and develop the ideas in the text. A large appendix provides a mechanism for class projects and a reference for readers who want the details of the algorithms. Practitioners may use this book for self-study and reference. For complete understanding, readers should have a background in calculus and linear algebra. The book does contain background material in multivariable calculus and numerical linear algebra.

Optimization
Optimization

Author: Rajesh Kumar Arora

Publisher: CRC Press

Published: 2015-05-06

Total Pages: 454

ISBN-13: 149872115X

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Choose the Correct Solution Method for Your Optimization ProblemOptimization: Algorithms and Applications presents a variety of solution techniques for optimization problems, emphasizing concepts rather than rigorous mathematical details and proofs. The book covers both gradient and stochastic methods as solution techniques for unconstrained and co

Comprehensive Chemometrics
Comprehensive Chemometrics

Author:

Publisher: Elsevier

Published: 2009-03-09

Total Pages: 2880

ISBN-13: 044452701X

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Designed to serve as the first point of reference on the subject, Comprehensive Chemometrics presents an integrated summary of the present state of chemical and biochemical data analysis and manipulation. The work covers all major areas ranging from statistics to data acquisition, analysis, and applications. This major reference work provides broad-ranging, validated summaries of the major topics in chemometrics—with chapter introductions and advanced reviews for each area. The level of material is appropriate for graduate students as well as active researchers seeking a ready reference on obtaining and analyzing scientific data. Features the contributions of leading experts from 21 countries, under the guidance of the Editors-in-Chief and a team of specialist Section Editors: L. Buydens; D. Coomans; P. Van Espen; A. De Juan; J.H. Kalivas; B.K. Lavine; R. Leardi; R. Phan-Tan-Luu; L.A. Sarabia; and J. Trygg Examines the merits and limitations of each technique through practical examples and extensive visuals: 368 tables and more than 1,300 illustrations (750 in full color) Integrates coverage of chemical and biological methods, allowing readers to consider and test a range of techniques Consists of 2,200 pages and more than 90 review articles, making it the most comprehensive work of its kind Offers print and online purchase options, the latter of which delivers flexibility, accessibility, and usability through the search tools and other productivity-enhancing features of ScienceDirect

Optimization Theory and Methods
Optimization Theory and Methods

Author: Wenyu Sun

Publisher: Springer Science & Business Media

Published: 2006-08-06

Total Pages: 689

ISBN-13: 0387249761

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Optimization Theory and Methods can be used as a textbook for an optimization course for graduates and senior undergraduates. It is the result of the author's teaching and research over the past decade. It describes optimization theory and several powerful methods. For most methods, the book discusses an idea’s motivation, studies the derivation, establishes the global and local convergence, describes algorithmic steps, and discusses the numerical performance.

Engineering Mathematics with Examples and Applications
Engineering Mathematics with Examples and Applications

Author: Xin-She Yang

Publisher: Academic Press

Published: 2016-12-29

Total Pages: 402

ISBN-13: 012809902X

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Engineering Mathematics with Examples and Applications provides a compact and concise primer in the field, starting with the foundations, and then gradually developing to the advanced level of mathematics that is necessary for all engineering disciplines. Therefore, this book's aim is to help undergraduates rapidly develop the fundamental knowledge of engineering mathematics. The book can also be used by graduates to review and refresh their mathematical skills. Step-by-step worked examples will help the students gain more insights and build sufficient confidence in engineering mathematics and problem-solving. The main approach and style of this book is informal, theorem-free, and practical. By using an informal and theorem-free approach, all fundamental mathematics topics required for engineering are covered, and readers can gain such basic knowledge of all important topics without worrying about rigorous (often boring) proofs. Certain rigorous proof and derivatives are presented in an informal way by direct, straightforward mathematical operations and calculations, giving students the same level of fundamental knowledge without any tedious steps. In addition, this practical approach provides over 100 worked examples so that students can see how each step of mathematical problems can be derived without any gap or jump in steps. Thus, readers can build their understanding and mathematical confidence gradually and in a step-by-step manner. - Covers fundamental engineering topics that are presented at the right level, without worry of rigorous proofs - Includes step-by-step worked examples (of which 100+ feature in the work) - Provides an emphasis on numerical methods, such as root-finding algorithms, numerical integration, and numerical methods of differential equations - Balances theory and practice to aid in practical problem-solving in various contexts and applications