標(biāo)題: Titlebook: NumericalInfinities and Infinitesimals in Optimization; Yaroslav D. Sergeyev,Renato De Leone Book 2022 The Editor(s) (if applicable) and T [打印本頁] 作者: CAP 時間: 2025-3-21 17:00
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作者: SUGAR 時間: 2025-3-21 23:06 作者: Charlatan 時間: 2025-3-22 04:07
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.作者: 送秋波 時間: 2025-3-22 06:06 作者: savage 時間: 2025-3-22 08:52 作者: amorphous 時間: 2025-3-22 14:10
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.作者: Statins 時間: 2025-3-22 20:57 作者: Pander 時間: 2025-3-22 23:35
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.作者: 沙發(fā) 時間: 2025-3-23 03:54 作者: 大門在匯總 時間: 2025-3-23 08:59 作者: 補助 時間: 2025-3-23 11:32
On the Use of Grossone Methodology for Handling Priorities in Multi-objective Evolutionary Optimizatinite and infinitesimal numbers. Most interestingly, this technique can be easily embedded in most of the existing evolutionary algorithms, without altering their core logic. Three algorithms for MPL-MOPs are shown: the first two, called PC-NSGA-II and PC-MOEA/D, are the generalization of NSGA-II an作者: 整體 時間: 2025-3-23 14:36
Exact Numerical Differentiation on?the?Infinity Computer and?Applications in?Global Optimizationise quadratic support functions and their convergence conditions are discussed. All the methods are implemented both in the traditional floating-point arithmetic and in the Infinity Computing framework.作者: 沉默 時間: 2025-3-23 21:14
Comparing Linear and Spherical Separation Using Grossone-Based Numerical Infinities in Classificatio selected far from both the two sets, obtaining in this way a kind of linear separation. This approach is easily extensible to the margin concept (of the type adopted in the Support Vector Machine technique) and to MIL problems. Some numerical results are reported on classical binary datasets drawn 作者: Gleason-score 時間: 2025-3-23 23:37
Computing Optimal Decision Strategies Using the Infinity Computer: The Case of Non-Archimedean Zero-Simplex algorithm called Gross-Matrix-Simplex. Four numerical experiments served as test cases to verify the effectiveness and correctness of the new algorithm. Moreover, these studies helped in stressing the difference between numerical and symbolic calculations: indeed, the solution output by the 作者: frugal 時間: 2025-3-24 03:38 作者: agitate 時間: 2025-3-24 07:50
NumericalInfinities and Infinitesimals in Optimization作者: 慢慢啃 時間: 2025-3-24 10:49
2194-7287 omputerscience..“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 Univer978-3-030-93644-0978-3-030-93642-6Series ISSN 2194-7287 Series E-ISSN 2194-7295 作者: 冬眠 時間: 2025-3-24 16:58
Marco Cococcioni,Alessandro Cudazzo,Massimo Pappalardo,Yaroslav D. Sergeyev作者: 是剝皮 時間: 2025-3-24 21:34
Manlio Gaudioso,Giovanni Giallombardo,Marat S. Mukhametzhanov作者: 血統(tǒng) 時間: 2025-3-24 23:46
Leonardo Lai,Lorenzo Fiaschi,Marco Cococcioni,Kalyanmoy Deb作者: chisel 時間: 2025-3-25 03:31 作者: Neutral-Spine 時間: 2025-3-25 09:05 作者: 斥責(zé) 時間: 2025-3-25 12:57 作者: excrete 時間: 2025-3-25 19:40
The Role of?, in?Nonlinear Programming and?Exact Penalty Methodsned optimization problem can be transformed in an “equivalent” unconstrained problem. In this chapter we show how . can be utilized in constructing exact differentiable penalty functions for the case of only equality constraints, the general case of equality and inequality constraints, and quadratic作者: archaeology 時間: 2025-3-25 21:50
Krylov-Subspace Methods for Quadratic Hypersurfaces: A Grossone–based Perspectivelinear systems. We preliminarily explore the relationship between the Conjugate Gradient (CG) method and the Lanczos process, along with their specific role of yielding tridiagonal matrices which retain large information on the original linear system matrix. Then, we show that on one hand there is n作者: 混亂生活 時間: 2025-3-26 00:50
Multi-objective Lexicographic Mixed-Integer Linear Programming: An Infinity Computer Approach one, by using the Grossone Methodology. Then we provide a simplex-like algorithm, called GrossSimplex, able to solve the original LMOLP problem using a single run of the algorithm (its theoretical correctness is also provided). In the second part, we tackle a Mixed-Integer Lexicographic Multi-Objec作者: 笨拙的我 時間: 2025-3-26 07:58 作者: COMA 時間: 2025-3-26 08:46
The Grossone-Based Diagonal Bundle Methodlass of unconstrained nonsmooth optimization methods based on a variable metric approach, where the use of the infinity computing techniques allows one to numerically deal with quantities which can take arbitrarily small or large values, as a consequence of nonsmoothness. In particular, choosing a d作者: aggressor 時間: 2025-3-26 16:25 作者: FOR 時間: 2025-3-26 16:53
Exact Numerical Differentiation on?the?Infinity Computer and?Applications in?Global OptimizationA novel way to efficiently compute . derivatives (the word “exact” means here with respect to the accuracy of the implementation of .(.)) is presented in this Chapter. It uses a new kind of a supercomputer—the Infinity Computer—able to work numerically with different finite, infinite, and infinitesi作者: 巫婆 時間: 2025-3-26 21:05
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作者: palette 時間: 2025-3-27 03:45
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作者: 變態(tài) 時間: 2025-3-27 07:29 作者: ALIEN 時間: 2025-3-27 11:21
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作者: chronicle 時間: 2025-3-27 16:35
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作者: 致命 時間: 2025-3-27 17:50
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作者: Ingratiate 時間: 2025-3-27 22:37 作者: narcissism 時間: 2025-3-28 02:51
NumericalInfinities and Infinitesimals in Optimization978-3-030-93642-6Series ISSN 2194-7287 Series E-ISSN 2194-7295 作者: Condescending 時間: 2025-3-28 10:20
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.作者: ANNUL 時間: 2025-3-28 11:34
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.作者: 漂亮 時間: 2025-3-28 14:41 作者: 神圣在玷污 時間: 2025-3-28 19:24 作者: Blood-Vessels 時間: 2025-3-29 00:17
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