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Applications of Conic Programming in Non-smooth Mechanics

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  • Jeremy Bleyer

    (Laboratoire Navier, ENPC, Univ Gustave Eiffel, CNRS)

Abstract

In the field of nonlinear mechanics, many challenging problems (e.g., plasticity, contact, masonry structures, nonlinear membranes) turn out to be expressible as conic programs. In general, such problems are non-smooth in nature (plasticity condition, unilateral condition, etc.), which makes their numerical resolution through standard Newton methods quite difficult. Their formulation as conic programs alleviates this difficulty since large-scale conic optimization problems can now be solved in a very robust and efficient manner, thanks to the development of dedicated interior-point algorithms. In this contribution, we review old and novel formulations of various non-smooth mechanics problems including associated plasticity with nonlinear hardening, nonlinear membranes, minimal crack surfaces, and viscoplastic fluid flows.

Suggested Citation

  • Jeremy Bleyer, 2024. "Applications of Conic Programming in Non-smooth Mechanics," Journal of Optimization Theory and Applications, Springer, vol. 202(1), pages 340-372, July.
    • Handle: RePEc:spr:joptap:v:202:y:2024:i:1:d:10.1007_s10957-022-02105-z
    DOI: 10.1007/s10957-022-02105-z
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    References listed on IDEAS

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    1. C. D. Bisbos & P. M. Pardalos, 2007. "Second-Order Cone and Semidefinite Representations of Material Failure Criteria," Journal of Optimization Theory and Applications, Springer, vol. 134(2), pages 275-301, August.
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