论文标题
质量优化问题与凸成本
Mass optimization problem with convex cost
论文作者
论文摘要
在本文中，我们考虑了在标量状态函数的情况下，我们考虑了质量优化问题，在这种情况下，我们没有对竞争对手的总质量施加限制，而是通过在措施空间上定义的凸功能来惩罚经典的合规性。我们通过合适的PDE获得最佳解决方案的特征。这概括了线性成本的文献中考虑的案例，并适用于导体的优化，该导体的电导率非常低和非常高的成本既具有很高的成本，然后对非线性模型的研究变得相关。
In this paper we consider a mass optimization problem in the case of scalar state function, where instead of imposing a constraint on the total mass of the competitors, we penalize the classical compliance by a convex functional defined on the space of measures. We obtain a characterization of optimal solutions to the problem through a suitable PDE. This generalizes the case considered in the literature of a linear cost and applies to the optimization of a conductor where very low and very high conductivities have both a high cost, and then the study of nonlinear models becomes relevant.
