论文标题
用于凸优化的级别测定方法的扰动视图
A perturbation view of level-set methods for convex optimization
论文作者
论文摘要
凸优化的级别集合方法基于以下想法：某些问题可以被参数化，以便可以将其解决方案恢复为扎根过程的限制过程。这个想法一次又一次地出现在凸问题的一系列算法中。在这里，我们证明了强大的二元性是成功级别方法的必要条件。在没有强双重性的情况下，级别的方法可以识别出$ε$ - 不可行的点，这些点不会收敛到可行点，因为$ε$趋于零。级别的方法也被用作证明技术，以建立与Slater的约束资格不同的强大二元性条件。
Level-set methods for convex optimization are predicated on the idea that certain problems can be parameterized so that their solutions can be recovered as the limiting process of a root-finding procedure. This idea emerges time and again across a range of algorithms for convex problems. Here we demonstrate that strong duality is a necessary condition for the level-set approach to succeed. In the absence of strong duality, the level-set method identifies $ε$-infeasible points that do not converge to a feasible point as $ε$ tends to zero. The level-set approach is also used as a proof technique for establishing sufficient conditions for strong duality that are different from Slater's constraint qualification.
