Differentiable Optimization and Equation Solving PDF Download

Author: John L. Nazareth
Publisher: Springer Science & Business Media
ISBN: 0387217886
Category : Mathematics
Languages : en
Pages : 255

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Book Description
An overview of the dramatic reorganization in reaction to N. Karmakar’s seminal 1984 paper on algorithmic linear programming in the area of algorithmic differentiable optimization and equation-solving, or, more simply, algorithmic differentiable programming. Aimed at readers familiar with advanced calculus and numerical analysis.

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Languages : en
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Book Description

Author: John Nazareth
Publisher: Springer
ISBN: 9781475777413
Category : Mathematics
Languages : en
Pages : 256

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Book Description
An overview of the dramatic reorganization in reaction to N. Karmakar’s seminal 1984 paper on algorithmic linear programming in the area of algorithmic differentiable optimization and equation-solving, or, more simply, algorithmic differentiable programming. Aimed at readers familiar with advanced calculus and numerical analysis.

Author: Lawrence Nazareth
Publisher: Springer
ISBN: 9781468493887
Category : Mathematics
Languages : en
Pages : 0

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Book Description
This book introduces a general audience to the main facets of optimization. Very little mathematical background is assumed. It should appeal to students, teachers, and a general audience interested in how optimization affects their everyday life, such as people in business.

Author: N.Z. Shor
Publisher: Springer Science & Business Media
ISBN: 3642821189
Category : Science
Languages : en
Pages : 171

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Book Description
In recent years much attention has been given to the development of auto matic systems of planning, design and control in various branches of the national economy. Quality of decisions is an issue which has come to the forefront, increasing the significance of optimization algorithms in math ematical software packages for al,ltomatic systems of various levels and pur poses. Methods for minimizing functions with discontinuous gradients are gaining in importance and the ~xperts in the computational methods of mathematical programming tend to agree that progress in the development of algorithms for minimizing nonsmooth functions is the key to the con struction of efficient techniques for solving large scale problems. This monograph summarizes to a certain extent fifteen years of the author's work on developing generalized gradient methods for nonsmooth minimization. This work started in the department of economic cybernetics of the Institute of Cybernetics of the Ukrainian Academy of Sciences under the supervision of V.S. Mikhalevich, a member of the Ukrainian Academy of Sciences, in connection with the need for solutions to important, practical problems of optimal planning and design. In Chap. I we describe basic classes of nonsmooth functions that are dif ferentiable almost everywhere, and analyze various ways of defining generalized gradient sets. In Chap. 2 we study in detail various versions of the su bgradient method, show their relation to the methods of Fejer-type approximations and briefly present the fundamentals of e-subgradient methods.

Author: J. A. Tenreiro Machado
Publisher: Springer Nature
ISBN: 3030371417
Category : Mathematics
Languages : en
Pages : 231

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Book Description
This collection covers new aspects of numerical methods in applied mathematics, engineering, and health sciences. It provides recent theoretical developments and new techniques based on optimization theory, partial differential equations (PDEs), mathematical modeling and fractional calculus that can be used to model and understand complex behavior in natural phenomena. Specific topics covered in detail include new numerical methods for nonlinear partial differential equations, global optimization, unconstrained optimization, detection of HIV- Protease, modelling with new fractional operators, analysis of biological models, and stochastic modelling.

Author: John Lawrence Nazareth
Publisher: Springer Nature
ISBN: 3031217624
Category : Computers
Languages : en
Pages : 79

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Book Description
Numerical Algorithmic Science and Engineering (NAS&E), or more compactly, Numerical Algorithmics, is the theoretical and empirical study and the practical implementation and application of algorithms for solving finite-dimensional problems of a numeric nature. The variables of such problems are either discrete-valued, or continuous over the reals, or, and as is often the case, a combination of the two, and they may or may not have an underlying network/graph structure. This re-emerging discipline of numerical algorithmics within computer science is the counterpart of the now well-established discipline of numerical analysis within mathematics, where the latter’s emphasis is on infinite-dimensional, continuous numerical problems and their finite-dimensional, continuous approximates. A discussion of the underlying rationale for numerical algorithmics, its foundational models of computation, its organizational details, and its role, in conjunction with numerical analysis, in support of the modern modus operandi of scientific computing, or computational science & engineering, is the primary focus of this short monograph. It comprises six chapters, each with its own bibliography. Chapters 2, 3 and 6 present the book’s primary content. Chapters 1, 4, and 5 are briefer, and they provide contextual material for the three primary chapters and smooth the transition between them. Mathematical formalism has been kept to a minimum, and, whenever possible, visual and verbal forms of presentation are employed and the discussion enlivened through the use of motivating quotations and illustrative examples. The reader is expected to have a working knowledge of the basics of computer science, an exposure to basic linear algebra and calculus (and perhaps some real analysis), and an understanding of elementary mathematical concepts such as convexity of sets and functions, networks and graphs, and so on. Although this book is not suitable for use as the principal textbook for a course on numerical algorithmics (NAS&E), it will be of value as a supplementary reference for a variety of courses. It can also serve as the primary text for a research seminar. And it can be recommended for self-study of the foundations and organization of NAS&E to graduate and advanced undergraduate students with sufficient mathematical maturity and a background in computing. When departments of computer science were first created within universities worldwide during the middle of the twentieth century, numerical analysis was an important part of the curriculum. Its role within the discipline of computer science has greatly diminished over time, if not vanished altogether, and specialists in that area are now to be found mainly within other fields, in particular, mathematics and the physical sciences. A central concern of this monograph is the regrettable, downward trajectory of numerical analysis within computer science and how it can be arrested and suitably reconstituted. Resorting to a biblical metaphor, numerical algorithmics (NAS&E) as envisioned herein is neither old wine in new bottles, nor new wine in old bottles, but rather this re-emerging discipline is a decantation of an age-old vintage that can hopefully find its proper place within the larger arena of computer science, and at what appears now to be an opportune time.

Author: Neha Gupta
Publisher: CRC Press
ISBN: 1000469239
Category : Business & Economics
Languages : en
Pages : 252

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Book Description
This book presents fundamental concepts of optimization problems and its real-world applications in various fields. The core concepts of optimization, formulations and solution procedures of various real-world problems are provided in an easy-to-read manner. The unique feature of this book is that it presents unified knowledge of the modelling of real-world decision-making problems and provides the solution procedure using the appropriate optimization techniques. The book will help students, researchers, and faculty members to understand the need for optimization techniques for obtaining optimal solution for the decision-making problems. It provides a sound knowledge of modelling of real-world problems using optimization techniques. It is a valuable compendium of several optimization techniques for solving real-world application problems using optimization software LINGO. The book is useful for academicians, practitioners, students and researchers in the field of OR. It is written in simple language with a detailed explanation of the core concepts of optimization techniques. Readers of this book will understand the formulation of real-world problems and their solution procedures obtained using the appropriate optimization techniques.

Author: Asen L. Dontchev
Publisher: Springer
ISBN: 149391037X
Category : Mathematics
Languages : en
Pages : 495

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Book Description
The implicit function theorem is one of the most important theorems in analysis and its many variants are basic tools in partial differential equations and numerical analysis. This second edition of Implicit Functions and Solution Mappings presents an updated and more complete picture of the field by including solutions of problems that have been solved since the first edition was published, and places old and new results in a broader perspective. The purpose of this self-contained work is to provide a reference on the topic and to provide a unified collection of a number of results which are currently scattered throughout the literature. Updates to this edition include new sections in almost all chapters, new exercises and examples, updated commentaries to chapters and an enlarged index and references section.

Author: Alexander Gelbukh
Publisher: Springer
ISBN: 3540886362
Category : Computers
Languages : en
Pages : 1058

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Book Description
The Mexican International Conference on Artificial Intelligence (MICAI), a yearly international conference series organized by the Mexican Society for Artificial Intel- gence (SMIA), is a major international AI forum and the main event in the academic life of the country’s growing AI community. In 2008 Mexico celebrates the 50th an- versary of development of computer science in the country: in 1958 the first computer was installed at the National Autonomous University of Mexico (UNAM). Nowadays, computer science is the country’s fastest growing research area. The proceedings of the previous MICAI events were published by Springer in its Lecture Notes in Artificial Intelligence (LNAI) series, vol. 1793, 2313, 2972, 3789, 4293, and 4827. Since its foundation in 2000, the conference has been growing in popularity, and improving in quality. This volume contains the papers presented at the oral session of the 7th Mexican International Conference on Artificial Intelligence, MICAI 2008, held October 27–31, 2008, in Atizapán de Zaragoza, Mexico. The conference received for evaluation 363 submissions by 1,032 authors from 43 countries (see Tables 1 and 2). This volume contains revised versions of 94 papers by 308 authors from 28 countries selected - cording to the results of an international reviewing process. Thus the acceptance rate was 25.9%. The book is structured into 20 thematic fields representative of the main current areas of interest for the AI community, plus a section of invited papers: