Attraction in Numerical Minimization
Attraction in Numerical Minimization

Author: Adam B. Levy

Publisher: Springer

Published: 2018-12-07

Total Pages: 86

ISBN-13: 3030040496

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Numerical minimization of an objective function is analyzed in this book to understand solution algorithms for optimization problems. Multiset-mappings are introduced to engineer numerical minimization as a repeated application of an iteration mapping. Ideas from numerical variational analysis are extended to define and explore notions of continuity and differentiability of multiset-mappings, and prove a fixed-point theorem for iteration mappings. Concepts from dynamical systems are utilized to develop notions of basin size and basin entropy. Simulations to estimate basins of attraction, to measure and classify basin size, and to compute basin are included to shed new light on convergence behavior in numerical minimization. Graduate students, researchers, and practitioners in optimization and mathematics who work theoretically to develop solution algorithms will find this book a useful resource.

Encyclopedia of Optimization
Encyclopedia of Optimization

Author: Christodoulos A. Floudas

Publisher: Springer Science & Business Media

Published: 2008-09-04

Total Pages: 4646

ISBN-13: 0387747583

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The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Optimization by Vector Space Methods
Optimization by Vector Space Methods

Author: David G. Luenberger

Publisher: John Wiley & Sons

Published: 1997-01-23

Total Pages: 348

ISBN-13: 9780471181170

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Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book.

Attractive Ellipsoids in Robust Control
Attractive Ellipsoids in Robust Control

Author: Alexander Poznyak

Publisher: Springer

Published: 2014-09-29

Total Pages: 365

ISBN-13: 3319092103

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This monograph introduces a newly developed robust-control design technique for a wide class of continuous-time dynamical systems called the “attractive ellipsoid method.” Along with a coherent introduction to the proposed control design and related topics, the monograph studies nonlinear affine control systems in the presence of uncertainty and presents a constructive and easily implementable control strategy that guarantees certain stability properties. The authors discuss linear-style feedback control synthesis in the context of the above-mentioned systems. The development and physical implementation of high-performance robust-feedback controllers that work in the absence of complete information is addressed, with numerous examples to illustrate how to apply the attractive ellipsoid method to mechanical and electromechanical systems. While theorems are proved systematically, the emphasis is on understanding and applying the theory to real-world situations. Attractive Ellipsoids in Robust Control will appeal to undergraduate and graduate students with a background in modern systems theory as well as researchers in the fields of control engineering and applied mathematics.

Physics of Biological Membranes
Physics of Biological Membranes

Author: Patricia Bassereau

Publisher: Springer

Published: 2018-12-30

Total Pages: 616

ISBN-13: 3030006301

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This book mainly focuses on key aspects of biomembranes that have emerged over the past 15 years. It covers static and dynamic descriptions, as well as modeling for membrane organization and shape at the local and global (at the cell level) scale. It also discusses several new developments in non-equilibrium aspects that have not yet been covered elsewhere. Biological membranes are the seat of interactions between cells and the rest of the world, and internally, they are at the core of complex dynamic reorganizations and chemical reactions. Despite the long tradition of membrane research in biophysics, the physics of cell membranes as well as of biomimetic or synthetic membranes is a rapidly developing field. Though successful books have already been published on this topic over the past decades, none include the most recent advances. Additionally, in this domain, the traditional distinction between biological and physical approaches tends to blur. This book gathers the most recent advances in this area, and will benefit biologists and physicists alike.

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.

The Basics of Practical Optimization
The Basics of Practical Optimization

Author: Adam B. Levy

Publisher: SIAM

Published: 2022-11-22

Total Pages: 179

ISBN-13: 1611977371

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Optimization is presented in most multivariable calculus courses as an application of the gradient, and while this treatment makes sense for a calculus course, there is much more to the theory of optimization. Optimization problems are generated constantly, and the theory of optimization has grown and developed in response to the challenges presented by these problems. This textbook aims to show readers how optimization is done in practice and help them to develop an appreciation for the richness of the theory behind the practice. Exercises, problems (including modeling and computational problems), and implementations are incorporated throughout the text to help students learn by doing. Python notes are inserted strategically to help readers complete computational problems and implementations. The Basics of Practical Optimization, Second Edition is intended for undergraduates who have completed multivariable calculus, as well as anyone interested in optimization. The book is appropriate for a course that complements or replaces a standard linear programming course.

Models and Algorithms for Global Optimization
Models and Algorithms for Global Optimization

Author: Aimo Törn

Publisher: Springer Science & Business Media

Published: 2007-04-08

Total Pages: 362

ISBN-13: 0387367217

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The research of Antanas Zilinskas has focused on developing models for global optimization, implementing and investigating the corresponding algorithms, and applying those algorithms to practical problems. This volume, dedicated to Professor Zilinskas on the occasion of his 60th birthday, contains new survey papers in which leading researchers from the field present various models and algorithms for solving global optimization problems.