论文标题
$ l^α$ - 贝克曼问题的限制
$L^α$-Regularization of the Beckmann Problem
论文作者
论文摘要
我们研究了所谓的Beckmann形式中最佳运输的问题，即在紧凑型集合上进行了两个ra尺度，我们寻求一个最佳流动场，该流量是在同一集合上描述这两种措施之间的流量并最小化某个线性成本函数的同一集合的矢量值ra。 我们认为问题的$ l^α$正规化，这可以确保唯一性并迫使解决方案成为可集成的函数，而不是ra量。这种正则化自然会产生半平滑的牛顿方案，该方案可用于数字解决问题。除了激励和开发数值方案外，我们还包括在连续环境中消失正则化的近似结果。
We investigate the problem of optimal transport in the so-called Beckmann form, i.e. given two Radon measures on a compact set, we seek an optimal flow field which is a vector valued Radon measure on the same set that describes a flow between these two measures and minimizes a certain linear cost function. We consider $L^α$ regularization of the problem, which guarantees uniqueness and forces the solution to be an integrable function rather than a Radon measure. This regularization naturally gives rise to a semi-smooth Newton scheme that can be used to solve the problem numerically. Besides motivating and developing the numerical scheme, we also include approximation results for vanishing regularization in the continuous setting.
