Accelerated proximal gradient method for elastoplastic analysis with von Mises yield criterion

  • Wataru Shimizu
  • Yoshihiro KannoEmail author
Original Paper Area 2


It is known that, under certain conditions, the quasi-static incremental analysis problem of elastoplastic structures with the von Mises yield criterion can be formulated as a second-order cone programming (SOCP) problem, which can be solved with a primal-dual interior-point method. Alternatively, this paper proposes to solve an equivalent unconstrained nonsmooth convex optimization problem, which has a form similar to a class of regularized least-square problems, known as group LASSO. We propose an accelerated proximal gradient method with an adaptive restart scheme for solving this unconstrained optimization problem. The algorithm is easy to implement, and free from numerical solution of linear equations unlike conventional methods in computational mechanics. Numerical experiments suggest that the presented algorithm outperforms a standard solver that implements a primal-dual interior-point method for conic optimization.


Second-order cone programming Accelerated gradient scheme Proximal gradient method Group LASSO Plasticity Incremental analysis 

Mathematics Subject Classification

90C25 65K10 90C90 



The work of the second author is partially supported by JSPS KAKENHI 26420545 and 17K06633.


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Copyright information

© The JJIAM Publishing Committee and Springer Japan KK 2017

Authors and Affiliations

  1. 1.Department of Mathematical Informatics, Graduate School of Information Science and TechnologyThe University of TokyoTokyoJapan
  2. 2.IHI CorporationTokyoJapan
  3. 3.Mathematics and Informatics CenterThe University of TokyoTokyoJapan

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