Aiming at optimizing the shape of closed embedded curves within prescribed isotopy classes, we use a gradient-based approach to approximate stationary points of the M\"obius energy. The gradients are computed with respect to Sobolev inner products similar to the $W^{3/2,2}$-inner product. This leads to optimization methods that are significantly more efficient and robust than standard techniques based on $L^2$-gradients.

翻译：为了在规定的等顶级内优化封闭嵌入曲线的形状,我们对M\“obius”能量的大约固定点采用了梯度法。对于Sobolev内产产品,其梯度的计算方法类似于$W3/2/2,2}内产产品。这导致优化方法比基于$L2美元梯度的标准技术更高效、更稳健。