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Bachelor Thesis from the year 2018 in the subject Mathematics - Applied Mathematics, Nanyang Technological University, language: English, abstract: This study aims to focus on a new approach to the Dividing Rectangles or DIRECT algorithm, which is used to solve multi-dimensional global optimization problems. It also delves into the resolution of DIRECT's combinatorial complexity in higher dimensions by transforming the problem domain into its one-dimensional equivalent. Many real-world problems involve multivariate global optimization which can be difficult to solve. In this report, a new approach to the Dividing Rectangles or DIRECT algorithm for solving multi-dimensional global optimization problems with bounds and a real-valued objective function, is discussed. DIRECT is a variation of the standard Lipschitzian optimization omitting the requirement of having to specify a Lipschitz constant; by viewing the Lipschitzian constant as a weighting parameter for indicating the emphasis to be placed on global versus local search. Typically, this constant is not so small in standard Lipschitz approaches, since the constant needs be at least as large as the maximum rate of change of the objective function; which forces a higher emphasis on global search and thus, results in a slower convergence. However, DIRECT enables operation at both global and local level by concurrently searching using all possible constants. The global part of the algorithm figures out the basin of convergence of the optimum, which the local part of the algorithm can suitably exploit. This justifies the fast convergence of DIRECT in computing the approximate minimum with the guaranteed precision. One major drawback of DIRECT is its combinatorial complexity in higher dimensions where DIRECT often takes many more function evaluations to find a good approximation of the global minimum. One method to resolve this difficulty is to transform the problem domain into its one-dimensional equivalent. This ap
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Leveraging Space-Filling Curves and the DIRECT Algorithm. A Novel Approach to Derivative-Free Multi-Dimensional Global Optimization
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GRIN Verlag Jul 2023, 2023
ISBN 10: 3346913767
ISBN 13: 9783346913760
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Librería: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Alemania
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Taschenbuch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Bachelor Thesis from the year 2018 in the subject Mathematics - Applied Mathematics, Nanyang Technological University, language: English, abstract: This study aims to focus on a new approach to the Dividing Rectangles or DIRECT algorithm, which is used to solve multi-dimensional global optimization problems. It also delves into the resolution of DIRECT's combinatorial complexity in higher dimensions by transforming the problem domain into its one-dimensional equivalent.Many real-world problems involve multivariate global optimization which can be difficult to solve. In this report, a new approach to the Dividing Rectangles or DIRECT algorithm for solving multi-dimensional global optimization problems with bounds and a real-valued objective function, is discussed. DIRECT is a variation of the standard Lipschitzian optimization omitting the requirement of having to specify a Lipschitz constant; by viewing the Lipschitzian constant as a weighting parameter for indicating the emphasis to be placed on global versus local search. Typically, this constant is not so small in standard Lipschitz approaches, since the constant needs be at least as large as the maximum rate of change of the objective function; which forces a higher emphasis on global search and thus, results in a slower convergence. However, DIRECT enables operation at both global and local level by concurrently searching using all possible constants. The global part of the algorithm figures out the basin of convergence of the optimum, which the local part of the algorithm can suitably exploit. This justifies the fast convergence of DIRECT in computing the approximate minimum with the guaranteed precision. One major drawback of DIRECT is its combinatorial complexity in higher dimensions where DIRECT often takes many more function evaluations to find a good approximation of the global minimum. One method to resolve this difficulty is to transform the problem domain into its one-dimensional equivalent. This approach is demonstrated in this report using space filling curves, to reduce the multiextremal optimization problem to the minimization of a univariate function. In this case, the Hölder continuity of space filling curves has been exploited to solve global optimization problems. 48 pp. Englisch. Nº de ref. del artículo: 9783346913760
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Leveraging Space-Filling Curves and the DIRECT Algorithm. A Novel Approach to Derivative-Free Multi-Dimensional Global Optimization
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Taschenbuch. Condición: Neu. Druck auf Anfrage Neuware - Printed after ordering - Bachelor Thesis from the year 2018 in the subject Mathematics - Applied Mathematics, Nanyang Technological University, language: English, abstract: This study aims to focus on a new approach to the Dividing Rectangles or DIRECT algorithm, which is used to solve multi-dimensional global optimization problems. It also delves into the resolution of DIRECT's combinatorial complexity in higher dimensions by transforming the problem domain into its one-dimensional equivalent.Many real-world problems involve multivariate global optimization which can be difficult to solve. In this report, a new approach to the Dividing Rectangles or DIRECT algorithm for solving multi-dimensional global optimization problems with bounds and a real-valued objective function, is discussed. DIRECT is a variation of the standard Lipschitzian optimization omitting the requirement of having to specify a Lipschitz constant; by viewing the Lipschitzian constant as a weighting parameter for indicating the emphasis to be placed on global versus local search. Typically, this constant is not so small in standard Lipschitz approaches, since the constant needs be at least as large as the maximum rate of change of the objective function; which forces a higher emphasis on global search and thus, results in a slower convergence. However, DIRECT enables operation at both global and local level by concurrently searching using all possible constants. The global part of the algorithm figures out the basin of convergence of the optimum, which the local part of the algorithm can suitably exploit. This justifies the fast convergence of DIRECT in computing the approximate minimum with the guaranteed precision. One major drawback of DIRECT is its combinatorial complexity in higher dimensions where DIRECT often takes many more function evaluations to find a good approximation of the global minimum. One method to resolve this difficulty is to transform the problem domain into its one-dimensional equivalent. This approach is demonstrated in this report using space filling curves, to reduce the multiextremal optimization problem to the minimization of a univariate function. In this case, the Hölder continuity of space filling curves has been exploited to solve global optimization problems. Nº de ref. del artículo: 9783346913760
Cantidad disponible: 1 disponibles
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Leveraging Space-Filling Curves and the DIRECT Algorithm. A Novel Approach to Derivative-Free Multi-Dimensional Global Optimization
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Leveraging Space-Filling Curves and the DIRECT Algorithm. A Novel Approach to Derivative-Free Multi-Dimensional Global Optimization
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Leveraging Space-Filling Curves and the DIRECT Algorithm. A Novel Approach to Derivative-Free Multi-Dimensional Global Optimization
Publicado por
GRIN Verlag, GRIN Verlag Jul 2023, 2023
ISBN 10: 3346913767
ISBN 13: 9783346913760
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Librería: buchversandmimpf2000, Emtmannsberg, BAYE, Alemania
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Taschenbuch. Condición: Neu. Neuware -Bachelor Thesis from the year 2018 in the subject Mathematics - Applied Mathematics, Nanyang Technological University, language: English, abstract: This study aims to focus on a new approach to the Dividing Rectangles or DIRECT algorithm, which is used to solve multi-dimensional global optimization problems. It also delves into the resolution of DIRECT's combinatorial complexity in higher dimensions by transforming the problem domain into its one-dimensional equivalent.Many real-world problems involve multivariate global optimization which can be difficult to solve. In this report, a new approach to the Dividing Rectangles or DIRECT algorithm for solving multi-dimensional global optimization problems with bounds and a real-valued objective function, is discussed. DIRECT is a variation of the standard Lipschitzian optimization omitting the requirement of having to specify a Lipschitz constant; by viewing the Lipschitzian constant as a weighting parameter for indicating the emphasis to be placed on global versus local search. Typically, this constant is not so small in standard Lipschitz approaches, since the constant needs be at least as large as the maximum rate of change of the objective function; which forces a higher emphasis on global search and thus, results in a slower convergence. However, DIRECT enables operation at both global and local level by concurrently searching using all possible constants. The global part of the algorithm figures out the basin of convergence of the optimum, which the local part of the algorithm can suitably exploit. This justifies the fast convergence of DIRECT in computing the approximate minimum with the guaranteed precision. One major drawback of DIRECT is its combinatorial complexity in higher dimensions where DIRECT often takes many more function evaluations to find a good approximation of the global minimum. One method to resolve this difficulty is to transform the problem domain into its one-dimensional equivalent. This approach is demonstrated in this report using space filling curves, to reduce the multiextremal optimization problem to the minimization of a univariate function. In this case, the Hölder continuity of space filling curves has been exploited to solve global optimization problems. 48 pp. Englisch. Nº de ref. del artículo: 9783346913760
Cantidad disponible: 2 disponibles
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Leveraging Space-Filling Curves and the DIRECT Algorithm. A Novel Approach to Derivative-Free Multi-Dimensional Global Optimization
Librería: preigu, Osnabrück, Alemania
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Taschenbuch. Condición: Neu. Leveraging Space-Filling Curves and the DIRECT Algorithm. A Novel Approach to Derivative-Free Multi-Dimensional Global Optimization | Aditi Dutta | Taschenbuch | Englisch | 2023 | GRIN Verlag | EAN 9783346913760 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu. Nº de ref. del artículo: 127360223
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