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Parametric Optimization of Metal Rod Structures Using the Modified Gradient Projection Method.

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Title: Parametric Optimization of Metal Rod Structures Using the Modified Gradient Projection Method.
Authors: Peleshko, I. D.1 (AUTHOR) ipeleshko@hotmail.com, Yurchenko, V. V.2 (AUTHOR)
Source: International Applied Mechanics. Jul2021, Vol. 57 Issue 4, p440-454. 15p.
Subjects: Nonlinear programming, Cost functions, Nonlinear equations, Absolute value, Mathematical optimization
Abstract: Problems of parametric optimization of rod structure stated in terms of the nonlinear programming problem are considered. Use is made of the method of projection of the gradient of the cost function onto the surface of active constraints while eliminating the residuals in the violated constraints. The equivalent Householder transformations are proposed for the governing equations of the optimization method. They ensure the computational efficiency of the algorithm based on the gradient method. In addition, the equivalent Givens transformations are also proposed for solving the equations of the method. They ensure, in the cases described in this article, the acceleration of the iterative process by reducing the amount of computation. The reliability of the optimal solutions obtained using the proposed modification of the gradient method is confirmed by comparing the results of optimization of rod systems. The efficiency of the proposed improvement of the optimization method is also confirmed by the obtained absolute values of the maximum residuals in the constraints in a small number of iterations. [ABSTRACT FROM AUTHOR]
Copyright of International Applied Mechanics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Parametric Optimization of Metal Rod Structures Using the Modified Gradient Projection Method.
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  Data: <searchLink fieldCode="JN" term="%22International+Applied+Mechanics%22">International Applied Mechanics</searchLink>. Jul2021, Vol. 57 Issue 4, p440-454. 15p.
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  Data: Problems of parametric optimization of rod structure stated in terms of the nonlinear programming problem are considered. Use is made of the method of projection of the gradient of the cost function onto the surface of active constraints while eliminating the residuals in the violated constraints. The equivalent Householder transformations are proposed for the governing equations of the optimization method. They ensure the computational efficiency of the algorithm based on the gradient method. In addition, the equivalent Givens transformations are also proposed for solving the equations of the method. They ensure, in the cases described in this article, the acceleration of the iterative process by reducing the amount of computation. The reliability of the optimal solutions obtained using the proposed modification of the gradient method is confirmed by comparing the results of optimization of rod systems. The efficiency of the proposed improvement of the optimization method is also confirmed by the obtained absolute values of the maximum residuals in the constraints in a small number of iterations. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of International Applied Mechanics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s10778-021-01096-0
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      – SubjectFull: Cost functions
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      – SubjectFull: Absolute value
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      – TitleFull: Parametric Optimization of Metal Rod Structures Using the Modified Gradient Projection Method.
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              Text: Jul2021
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