Fundamentals of Optimization

Fundamentals of Optimization

Author: Mark French

Publisher: Springer

Published: 2018-05-02

Total Pages: 255

ISBN-13: 3319761927

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This textbook is for readers new or returning to the practice of optimization whose interest in the subject may relate to a wide range of products and processes. Rooted in the idea of “minimum principles,” the book introduces the reader to the analytical tools needed to apply optimization practices to an array of single- and multi-variable problems. While comprehensive and rigorous, the treatment requires no more than a basic understanding of technical math and how to display mathematical results visually. It presents a group of simple, robust methods and illustrates their use in clearly-defined examples. Distinct from the majority of optimization books on the market intended for a mathematically sophisticated audience who might want to develop their own new methods of optimization or do research in the field, this volume fills the void in instructional material for those who need to understand the basic ideas. The text emerged from a set of applications-driven lecture notes used in optimization courses the author has taught for over 25 years. The book is class-tested and refined based on student feedback, devoid of unnecessary abstraction, and ideal for students and practitioners from across the spectrum of engineering disciplines. It provides context through practical examples and sections describing commercial application of optimization ideas, such as how containerized freight and changing sea routes have been used to continually reduce the cost of moving freight across oceans. It also features 2D and 3D plots and an appendix illustrating the most widely used MATLAB optimization functions.


Fundamentals of Optimization Techniques with Algorithms

Fundamentals of Optimization Techniques with Algorithms

Author: Sukanta Nayak

Publisher: Academic Press

Published: 2020-08-25

Total Pages: 323

ISBN-13: 0128224924

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Optimization is a key concept in mathematics, computer science, and operations research, and is essential to the modeling of any system, playing an integral role in computer-aided design. Fundamentals of Optimization Techniques with Algorithms presents a complete package of various traditional and advanced optimization techniques along with a variety of example problems, algorithms and MATLAB© code optimization techniques, for linear and nonlinear single variable and multivariable models, as well as multi-objective and advanced optimization techniques. It presents both theoretical and numerical perspectives in a clear and approachable way. In order to help the reader apply optimization techniques in practice, the book details program codes and computer-aided designs in relation to real-world problems. Ten chapters cover, an introduction to optimization; linear programming; single variable nonlinear optimization; multivariable unconstrained nonlinear optimization; multivariable constrained nonlinear optimization; geometric programming; dynamic programming; integer programming; multi-objective optimization; and nature-inspired optimization. This book provides accessible coverage of optimization techniques, and helps the reader to apply them in practice. - Presents optimization techniques clearly, including worked-out examples, from traditional to advanced - Maps out the relations between optimization and other mathematical topics and disciplines - Provides systematic coverage of algorithms to facilitate computer coding - Gives MATLAB© codes in relation to optimization techniques and their use in computer-aided design - Presents nature-inspired optimization techniques including genetic algorithms and artificial neural networks


Foundations of Optimization

Foundations of Optimization

Author: Osman Güler

Publisher: Springer Science & Business Media

Published: 2010-08-03

Total Pages: 445

ISBN-13: 0387684077

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This book covers the fundamental principles of optimization in finite dimensions. It develops the necessary material in multivariable calculus both with coordinates and coordinate-free, so recent developments such as semidefinite programming can be dealt with.


Extremal Optimization

Extremal Optimization

Author: Yong-Zai Lu

Publisher: CRC Press

Published: 2018-09-03

Total Pages: 278

ISBN-13: 1315360071

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Extremal Optimization: Fundamentals, Algorithms, and Applications introduces state-of-the-art extremal optimization (EO) and modified EO (MEO) solutions from fundamentals, methodologies, and algorithms to applications based on numerous classic publications and the authors’ recent original research results. It promotes the movement of EO from academic study to practical applications. The book covers four aspects, beginning with a general review of real-world optimization problems and popular solutions with a focus on computational complexity, such as "NP-hard" and the "phase transitions" occurring on the search landscape. Next, it introduces computational extremal dynamics and its applications in EO from principles, mechanisms, and algorithms to the experiments on some benchmark problems such as TSP, spin glass, Max-SAT (maximum satisfiability), and graph partition. It then presents studies on the fundamental features of search dynamics and mechanisms in EO with a focus on self-organized optimization, evolutionary probability distribution, and structure features (e.g., backbones), which are based on the authors’ recent research results. Finally, it discusses applications of EO and MEO in multiobjective optimization, systems modeling, intelligent control, and production scheduling. The authors present the advanced features of EO in solving NP-hard problems through problem formulation, algorithms, and simulation studies on popular benchmarks and industrial applications. They also focus on the development of MEO and its applications. This book can be used as a reference for graduate students, research developers, and practical engineers who work on developing optimization solutions for those complex systems with hardness that cannot be solved with mathematical optimization or other computational intelligence, such as evolutionary computations.


Nonlinear and Mixed-Integer Optimization

Nonlinear and Mixed-Integer Optimization

Author: Christodoulos A. Floudas

Publisher: Oxford University Press

Published: 1995-10-05

Total Pages: 475

ISBN-13: 0195100565

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This volume presents the fundamentals of nonlinear and mixed-integer optimisation, and their applications in the important area of process synthesis in chemical engineering. Topics that are unique include the theory and methods for mixed-integer nonlinear optimisation, introduction to modelling issues in process synthesis, and optimisation-based approaches in the synthesis of heat recovery systems, distillation-based systems, and reactor-based systems.


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.


Optimization Theory with Applications

Optimization Theory with Applications

Author: Donald A. Pierre

Publisher: Courier Corporation

Published: 2012-07-12

Total Pages: 644

ISBN-13: 0486136957

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Broad-spectrum approach to important topic. Explores the classic theory of minima and maxima, classical calculus of variations, simplex technique and linear programming, optimality and dynamic programming, more. 1969 edition.


Optimization in Engineering

Optimization in Engineering

Author: Ramteen Sioshansi

Publisher: Springer

Published: 2017-06-24

Total Pages: 422

ISBN-13: 3319567691

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This textbook covers the fundamentals of optimization, including linear, mixed-integer linear, nonlinear, and dynamic optimization techniques, with a clear engineering focus. It carefully describes classical optimization models and algorithms using an engineering problem-solving perspective, and emphasizes modeling issues using many real-world examples related to a variety of application areas. Providing an appropriate blend of practical applications and optimization theory makes the text useful to both practitioners and students, and gives the reader a good sense of the power of optimization and the potential difficulties in applying optimization to modeling real-world systems. The book is intended for undergraduate and graduate-level teaching in industrial engineering and other engineering specialties. It is also of use to industry practitioners, due to the inclusion of real-world applications, opening the door to advanced courses on both modeling and algorithm development within the industrial engineering and operations research fields.


Practical Augmented Lagrangian Methods for Constrained Optimization

Practical Augmented Lagrangian Methods for Constrained Optimization

Author: Ernesto G. Birgin

Publisher: SIAM

Published: 2014-04-30

Total Pages: 222

ISBN-13: 161197335X

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This book focuses on Augmented Lagrangian techniques for solving practical constrained optimization problems. The authors rigorously delineate mathematical convergence theory based on sequential optimality conditions and novel constraint qualifications. They also orient the book to practitioners by giving priority to results that provide insight on the practical behavior of algorithms and by providing geometrical and algorithmic interpretations of every mathematical result, and they fully describe a freely available computational package for constrained optimization and illustrate its usefulness with applications.


Convex Optimization for Signal Processing and Communications

Convex Optimization for Signal Processing and Communications

Author: Chong-Yung Chi

Publisher: CRC Press

Published: 2017-01-24

Total Pages: 294

ISBN-13: 1315349809

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Convex Optimization for Signal Processing and Communications: From Fundamentals to Applications provides fundamental background knowledge of convex optimization, while striking a balance between mathematical theory and applications in signal processing and communications. In addition to comprehensive proofs and perspective interpretations for core convex optimization theory, this book also provides many insightful figures, remarks, illustrative examples, and guided journeys from theory to cutting-edge research explorations, for efficient and in-depth learning, especially for engineering students and professionals. With the powerful convex optimization theory and tools, this book provides you with a new degree of freedom and the capability of solving challenging real-world scientific and engineering problems.