Subgradient ellipsoid method for nonsmooth convex problems
提出一种结合次梯度法与椭球法的新算法，用于求解非光滑凸最小化、凸凹鞍点及单调变分不等式问题，在高维下仍保持合理收敛速度，并引入高效精度认证技术。
In this paper, we present a new ellipsoid-type algorithm for solving nonsmooth problems with convex structure. Examples of such problems include nonsmooth convex minimization problems, convex-concave saddle-point problems and variational inequalities with monotone operator. Our algorithm can be seen as a combination of the standard Subgradient and Ellipsoid methods. However, in contrast to the latter one, the proposed method has a reasonable convergence rate even when the dimensionality of the problem is sufficiently large. For generating accuracy certificates in our algorithm, we propose an efficient technique, which ameliorates the previously known recipes (Nemirovski in Math Oper Res 35(1):52-78, 2010).