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Titlebook: NumericalInfinities and Infinitesimals in Optimization; Yaroslav D. Sergeyev,Renato De Leone Book 2022 The Editor(s) (if applicable) and T

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书目名称NumericalInfinities and Infinitesimals in Optimization
编辑Yaroslav D. Sergeyev,Renato De Leone
视频video
概述Presents a new powerful supercomputing paradigm introduced by Yaroslav D. Sergeyev.Gives friendly introduction to the paradigm and proposes a broad panorama of a successful usage of numerical infiniti
丛书名称Emergence, Complexity and Computation
图书封面Titlebook: NumericalInfinities and Infinitesimals in Optimization;  Yaroslav D. Sergeyev,Renato De Leone Book 2022 The Editor(s) (if applicable) and T
描述.This book provides a friendly introduction to the paradigm and proposes a broad panorama of killing applications of the Infinity Computer in optimization: radically new numerical algorithms, great theoretical insights, efficient software implementations, and interesting practical case studies. This is the first book presenting to the readers interested in optimization the advantages of a recently introduced supercomputing paradigm that allows to numerically work with different infinities and infinitesimals on the Infinity Computer patented in several countries. One of the editors of the book is the creator of the Infinity Computer, and another editor was the first who has started to use it in optimization. Their results were awarded by numerous scientific prizes. This engaging book opens new horizons for researchers, engineers, professors, and students with interests in supercomputing paradigms, optimization, decision making, game theory, and foundations of mathematics and computerscience..“Mathematicians have never been comfortable handling infinities… But an entirely new type of mathematics looks set to by-pass the problem… Today, Yaroslav Sergeyev, a mathematician at the Univer
出版日期Book 2022
关键词Optimization; Numerical Infinities; Infinity Computer; Software Implementations; Infinitesimals in Optim
版次1
doihttps://doi.org/10.1007/978-3-030-93642-6
isbn_softcover978-3-030-93644-0
isbn_ebook978-3-030-93642-6Series ISSN 2194-7287 Series E-ISSN 2194-7295
issn_series 2194-7287
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
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The Grossone-Based Diagonal Bundle Methodiagonal matrix with positive entries as a metric, we modify the so called Diagonal Bundle algorithm by means of matrix updates based on the infinity computing paradigm, and we provide the computational results obtained on a set of benchmark academic test-problems.
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Adopting the Infinity Computing in Simulink for Scientific Computing suitable for handling problems in control theory and dynamics, where visual programming environments like Simulink are commonly used. In this context, the chapter presents the ., a novel solution that allows one to exploit the Infinity Computer arithmetic within the Simulink environment.
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The Role of , in Nonlinear Programming and Exact Penalty Methodsimal solution of the unconstrained problem. Moreover, Lagrangian duals associated to the constraints are also automatically obtained from the infinitesimal terms. Finally a new algorithmic scheme is presented.
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