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Accelerated proximal gradient method for bi-modulus static elasticity
Bi-modulus constitutive law assumes that material constants have different values in tension and compression. It is known that finding an equilibrium state of an elastic body consisting of a bi-modulus material is recast as a semidefinite programming problem, which can be solved with a primal-dual interior-point method. As an alternative approach, this paper presents a fast first-order optimization method. Specifically, we propose an accelerated proximal gradient method for solving a minimization problem of the total potential energy. This algorithm is easy to implement, and free from numerical solution of linear equations. Numerical experiments demonstrate that the proposed method outperforms the semidefinite programming approach with a standard solver implementing a primal-dual interior-point method.
Accelerated proximal gradient method for bi-modulus static elasticity
Bi-modulus constitutive law assumes that material constants have different values in tension and compression. It is known that finding an equilibrium state of an elastic body consisting of a bi-modulus material is recast as a semidefinite programming problem, which can be solved with a primal-dual interior-point method. As an alternative approach, this paper presents a fast first-order optimization method. Specifically, we propose an accelerated proximal gradient method for solving a minimization problem of the total potential energy. This algorithm is easy to implement, and free from numerical solution of linear equations. Numerical experiments demonstrate that the proposed method outperforms the semidefinite programming approach with a standard solver implementing a primal-dual interior-point method.
Accelerated proximal gradient method for bi-modulus static elasticity
Optim Eng
Kanno, Yoshihiro (Autor:in)
Optimization and Engineering ; 23 ; 453-477
01.03.2022
25 pages
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
Bi-modulus material , Convex optimization , First-order optimization method , Proximal gradient method , Semidefinite programming Mathematics , Optimization , Engineering, general , Systems Theory, Control , Environmental Management , Operations Research/Decision Theory , Financial Engineering , Mathematics and Statistics
Correction to: Accelerated proximal gradient method for bi-modulus static elasticity
| Springer Verlag | 2024
Correction to: Accelerated proximal gradient method for bi-modulus static elasticity
| Springer Verlag | 2024
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