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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Comparing Linear and Spherical Separation Using Grossone-Based Numerical Infinities in Classificatioction with the use of the grossone-based numerical infinities. While in the binary supervised learning the objective is to separate two sets of samples, a binary MIL problem consists in separating two different type of sets (positive and negative), each of them constituted by a finite number of samp

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Computing Optimal Decision Strategies Using the Infinity Computer: The Case of Non-Archimedean Zero-ons and engineering, among others. In particular, the Nash equilibria of any two-player finite zero-sum game in mixed-strategies can be found solving a proper linear programming problem. This chapter investigates and solves non-Archimedean zero-sum games, i.e., games satisfying the zero-sum property

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ALIEN

Adopting the Infinity Computing in Simulink for Scientific Computingpoint standard to represent and work with real numbers. Due to the architectural limitations of traditional computers, it is impossible to handle infinite and infinitesimal quantities numerically. This chapter is devoted to the Infinity Computer, a supercomputer that permits to execute numerical com

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Addressing Ill-Conditioning in Global Optimization Using a Software Implementation of the Infinity Cly homogeneous if it produces the same sequences of evaluation points independently both of multiplication of the objective function by a scaling constant and of adding a shifting constant. It is shown that even if a method possesses this property theoretically, numerically very small and large scal

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Yaroslav D. Sergeyev,Renato De LeonePresents 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

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NumericalInfinities and Infinitesimals in Optimization978-3-030-93642-6Series ISSN 2194-7287 Series E-ISSN 2194-7295

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Nonlinear Optimization: A Brief Overviewto cover all the aspects in nonlinear optimization that will require more than one complete book. We decided, instead, to concentrate our attention on few fundamental topics that are also at the basis of the new results in nonlinear optimization using . introduced in the successive chapters.

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Modeling Infinite Games on Finite Graphs Using Numerical Infinities infinite games played on finite graphs using the Grossone paradigm. The new Grossone model provides certain advantages such as allowing for draws, which are common in board games, and a more accurate and decisive method for determining the winner.