论文标题
Gâteaux半渐进式方法应用于接触问题的形状优化
Gâteaux semiderivative approach applied to shape optimization for contact problems
论文作者
论文摘要
受变异不平等（VI）限制的形状优化问题是非平滑和非凸优化问题。由于变异不平等的约束而产生了非平滑度，这使得在得出最佳条件方面具有挑战性。除非平滑度外，还由于VIS以及分布式，非线性，非凸和无限维方面的互补方面，这是由于形状复杂而建立了最佳系统的形状，因此可以开发有效的解决方案算法。在本文中，我们考虑了Gâteaux半脱位，以制定最佳条件。在应用程序中，我们专注于受联系问题约束的形状优化问题。
Shape optimization problems constrained by variational inequalities (VI) are non-smooth and non-convex optimization problems. The non-smoothness arises due to the variational inequality constraint, which makes it challenging to derive optimality conditions. Besides the non-smoothness there are complementary aspects due to the VIs as well as distributed, non-linear, non-convex and infinite-dimensional aspects due to the shapes which complicate to set up an optimality system and, thus, to develop efficient solution algorithms. In this paper, we consider Gâteaux semiderivatives in order to formulate optimality conditions. In the application, we concentrate on a shape optimization problem constrained by the contact problem.
