论文标题
核标准球的平坦度，同时极化和核规范最小化的独特性
Flatness of the nuclear norm sphere, simultaneous polarization, and uniqueness in nuclear norm minimization
论文作者
论文摘要
在本文中，我们通过同时极化的概念和核定标准的细分表达来建立必要和充分的条件，以实现核定范围内的线段（或公寓）的存在。然后将其杠杆化以提供（基于点）的必要条件，以使解决方案的独特性最小化，以最大程度地减少仿射歧管上的核标准。我们进一步建立了一组唯一性的足够条件，基于核标准的细分差异和解决问题的线性操作员的范围的相互作用。最后，使用凸双重性，我们展示了如何将原始问题的唯一性结果转移到一类严格凸出的保真度项的一类核规范规范化的最小化问题上。
In this paper we establish necessary and sufficient conditions for the existence of line segments (or flats) in the sphere of the nuclear norm via the notion of simultaneous polarization and a refined expression for the subdifferential of the nuclear norm. This is then leveraged to provide (point-based) necessary and sufficient conditions for uniqueness of solutions for minimizing the nuclear norm over an affine manifold. We further establish an alternative set of sufficient conditions for uniqueness, based on the interplay of the subdifferential of the nuclear norm and the range of the problem-defining linear operator. Finally, using convex duality, we show how to transfer the uniqueness results for the original problem to a whole class of nuclear norm-regularized minimization problems with a strictly convex fidelity term.
