Elements Of Classical And Geometric Optimization

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Elements Of Classical And Geometric Optimization

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Author : Debasish Roy
language : en
Publisher: CRC Press
Release Date : 2024-01-25

Elements Of Classical And Geometric Optimization written by Debasish Roy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-25 with Technology & Engineering categories.

This comprehensive textbook covers both classical and geometric aspects of optimization using methods, deterministic and stochastic, in a single volume and in a language accessible to non-mathematicians. It will help serve as an ideal study material for senior undergraduate and graduate students in the fields of civil, mechanical, aerospace, electrical, electronics, and communication engineering. The book includes: Derivative-based Methods of Optimization. Direct Search Methods of Optimization. Basics of Riemannian Differential Geometry. Geometric Methods of Optimization using Riemannian Langevin Dynamics. Stochastic Analysis on Manifolds and Geometric Optimization Methods. This textbook comprehensively treats both classical and geometric optimization methods, including deterministic and stochastic (Monte Carlo) schemes. It offers an extensive coverage of important topics including derivative-based methods, penalty function methods, method of gradient projection, evolutionary methods, geometric search using Riemannian Langevin dynamics and stochastic dynamics on manifolds. The textbook is accompanied by online resources including MATLAB codes which are uploaded on our website. The textbook is primarily written for senior undergraduate and graduate students in all applied science and engineering disciplines and can be used as a main or supplementary text for courses on classical and geometric optimization.

Geometric Methods And Optimization Problems

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Author : Vladimir Boltyanski
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-12-31

Geometric Methods And Optimization Problems written by Vladimir Boltyanski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12-31 with Computers categories.

This book focuses on three disciplines of applied mathematics: control theory, location science and computational geometry. The authors show how methods and tools from convex geometry in a wider sense can help solve various problems from these disciplines. More precisely they consider mainly the tent method (as an application of a generalized separation theory of convex cones) in nonclassical variational calculus, various median problems in Euclidean and other Minkowski spaces (including a detailed discussion of the Fermat-Torricelli problem) and different types of partitionings of topologically complicated polygonal domains into a minimum number of convex pieces. Figures are used extensively throughout the book and there is also a large collection of exercises. Audience: Graduate students, teachers and researchers.

Shapes And Geometries

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Author : M. C. Delfour
language : en
Publisher: SIAM
Release Date : 2011-01-01

Shapes And Geometries written by M. C. Delfour and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-01 with Mathematics categories.

Presents the latest groundbreaking theoretical foundation to shape optimization in a form accessible to mathematicians, scientists and engineers.

Control Theory From The Geometric Viewpoint

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Author : Andrei A. Agrachev
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-04-15

Control Theory From The Geometric Viewpoint written by Andrei A. Agrachev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-15 with Language Arts & Disciplines categories.

This book presents some facts and methods of Mathematical Control Theory treated from the geometric viewpoint. It is devoted to finite-dimensional deterministic control systems governed by smooth ordinary differential equations. The problems of controllability, state and feedback equivalence, and optimal control are studied. Some of the topics treated by the authors are covered in monographic or textbook literature for the first time while others are presented in a more general and flexible setting than elsewhere. Although being fundamentally written for mathematicians, the authors make an attempt to reach both the practitioner and the theoretician by blending the theory with applications. They maintain a good balance between the mathematical integrity of the text and the conceptual simplicity that might be required by engineers. It can be used as a text for graduate courses and will become most valuable as a reference work for graduate students and researchers.

Convex Optimization

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Author : Stephen P. Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2004-03-08

Convex Optimization written by Stephen P. Boyd and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-08 with Business & Economics categories.

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.

Twentieth Anniversary Volume Discrete Computational Geometry

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Author : Jacob E. Goodman
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-02

Twentieth Anniversary Volume Discrete Computational Geometry written by Jacob E. Goodman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-02 with Mathematics categories.

This commemorative book contains the 28 major articles that appeared in the 2008 Twentieth Anniversary Issue of the journal Discrete & Computational Geometry, and presents a comprehensive picture of the current state of the field. The articles in this volume, a number of which solve long-outstanding problems in the field, were chosen by the editors of DCG for the importance of their results, for the breadth of their scope, and to show the intimate connections that have arisen between discrete and computational geometry and other areas of both computer science and mathematics. Apart from the articles, the editors present an expanded preface, along with a set of photographs of groups and individuals who have played a major role in the history of the field during the past twenty years.

Generative Design In Aerospace And Automotive Structures

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Author : Jody Emlyn Muelaner
language : en
Publisher: SAE International
Release Date : 2024-07-23

Generative Design In Aerospace And Automotive Structures written by Jody Emlyn Muelaner and has been published by SAE International this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-23 with Technology & Engineering categories.

Semi-automated computational design methods involving physics-based simulation, optimization, machine learning, and generative artificial intelligence (AI) already allow greatly enhanced performance alongside reduced cost in both design and manufacturing. As we progress, developments in user interfaces, AI integration, and automation of workflows will increasingly reduce the human inputs required to achieve this. With this, engineering teams must change their mindset from designing products to specifying requirements, focusing their efforts on testing and analysis to provide accurate specifications. Generative Design in Aerospace and Automotive Structures discusses generative design in its broadest sense, including the challenges and recommendations regarding multi-stage optimizations. Click here to access the full SAE EDGETM Research Report portfolio. https://doi.org/10.4271/EPR2024016

Computing And Software Science

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Author : Bernhard Steffen
language : en
Publisher: Springer Nature
Release Date : 2019-10-04

Computing And Software Science written by Bernhard Steffen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-04 with Computers categories.

The papers of this volume focus on the foundational aspects of computer science, the thematic origin and stronghold of LNCS, under the title “Computing and Software Science: State of the Art and Perspectives”. They are organized in two parts: The first part, Computation and Complexity, presents a collection of expository papers on fashionable themes in algorithmics, optimization, and complexity. The second part, Methods, Languages and Tools for Future System Development, aims at sketching the methodological evolution that helps guaranteeing that future systems meet their increasingly critical requirements. Chapter 3 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Geometric Algebra For Computer Science

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Author : Leo Dorst
language : en
Publisher: Elsevier
Release Date : 2010-07-26

Geometric Algebra For Computer Science written by Leo Dorst and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-26 with Computers categories.

Until recently, almost all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates, however, which can make many geometric programming tasks very specific and complex-often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming. Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. In this book you will find an introduction to GA that will give you a strong grasp of its relationship to linear algebra and its significance for your work. You will learn how to use GA to represent objects and perform geometric operations on them. And you will begin mastering proven techniques for making GA an integral part of your applications in a way that simplifies your code without slowing it down. * The first book on Geometric Algebra for programmers in computer graphics and entertainment computing* Written by leaders in the field providing essential information on this new technique for 3D graphics* This full colour book includes a website with GAViewer, a program to experiment with GA

Geometric Partial Differential Equations Part 2

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Author : Andrea Bonito
language : en
Publisher: Elsevier
Release Date : 2021-01-26

Geometric Partial Differential Equations Part 2 written by Andrea Bonito and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-26 with Mathematics categories.

Besides their intrinsic mathematical interest, geometric partial differential equations (PDEs) are ubiquitous in many scientific, engineering and industrial applications. They represent an intellectual challenge and have received a great deal of attention recently. The purpose of this volume is to provide a missing reference consisting of self-contained and comprehensive presentations. It includes basic ideas, analysis and applications of state-of-the-art fundamental algorithms for the approximation of geometric PDEs together with their impacts in a variety of fields within mathematics, science, and engineering. - About every aspect of computational geometric PDEs is discussed in this and a companion volume. Topics in this volume include stationary and time-dependent surface PDEs for geometric flows, large deformations of nonlinearly geometric plates and rods, level set and phase field methods and applications, free boundary problems, discrete Riemannian calculus and morphing, fully nonlinear PDEs including Monge-Ampere equations, and PDE constrained optimization - Each chapter is a complete essay at the research level but accessible to junior researchers and students. The intent is to provide a comprehensive description of algorithms and their analysis for a specific geometric PDE class, starting from basic concepts and concluding with interesting applications. Each chapter is thus useful as an introduction to a research area as well as a teaching resource, and provides numerous pointers to the literature for further reading - The authors of each chapter are world leaders in their field of expertise and skillful writers. This book is thus meant to provide an invaluable, readable and enjoyable account of computational geometric PDEs