Interior‐point methods (IPMs) are well suited for solving convex nonsmooth optimization problems which arise for instance in problems involving plasticity or contact conditions. This work attempts at extending their field of application to optimization problems involving either smooth but nonconvex or nonsmooth but convex objectives or constraints. A typical application for such kind of problems is finite‐strain elastoplasticity which we address using a total Lagrangian formulation based on logarithmic strain measures. The proposed interior‐point algorithm is implemented and tested on 3D examples involving plastic collapse and geometrical changes. Comparison with classical, Newton‐Raphson/return mapping methods show that the IPM exhibits good computational performance, especially in terms of convergence robustness. Similar to what is observed for convex small‐strain plasticity, the IPM is able to converge for much larger load steps than classical methods.

中文翻译：

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将内点方法扩展到非线性二阶锥规划：在有限应变弹塑性中的应用

内点法（IPM）非常适合解决凸面非光滑优化问题，例如在涉及塑性或接触条件的问题中出现的问题。这项工作试图将其应用领域扩展到涉及平滑但不凸或不平滑但凸目标或约束的优化问题。这类问题的典型应用是有限应变弹塑性，我们使用基于对数应变测度的总拉格朗日公式来解决。拟议的内点算法在涉及塑性塌陷和几何变化的3D实例上实施和测试。与经典牛顿-拉夫森/返回映射方法的比较表明，IPM具有良好的计算性能，尤其是在收敛鲁棒性方面。