论文标题
可变度量复合近端交替的线性最小化，用于非convex非平滑优化
Variable Metric Composite Proximal Alternating Linearized Minimization for Nonconvex Nonsmooth Optimization
论文作者
论文摘要
在本文中，我们提出了一种近端算法，用于最大程度地减少由三个术语组成的两个块变量的客观函数：1）平滑函数，2）非平滑函数，它是严格增加，凹面，可区分的函数和convex nonsmooth函数的组成，而convex nonsmooth函数和3）平滑函数可以使两个块变量构成。我们提出了一个可变的度量复合近端交替线性化最小化（CPALM）来解决此类问题。在强大的kurdyka-lojasiewicz属性的基础上，我们得出了融合分析，并确定CPALM在全球范围内生成的每个有界序列都会收敛到临界点。我们在平行磁共振图像重建问题上演示了CPALM方法。获得的数值结果显示了所提出方法的生存能力和有效性。
In this paper we propose a proximal algorithm for minimizing an objective function of two block variables consisting of three terms: 1) a smooth function, 2) a nonsmooth function which is a composition between a strictly increasing, concave, differentiable function and a convex nonsmooth function, and 3) a smooth function which couples the two block variables. We propose a variable metric composite proximal alternating linearized minimization (CPALM) to solve this class of problems. Building on the powerful Kurdyka-Łojasiewicz property, we derive the convergence analysis and establish that each bounded sequence generated by CPALM globally converges to a critical point. We demonstrate the CPALM method on parallel magnetic resonance image reconstruction problems. The obtained numerical results shows the viability and effectiveness of the proposed method.
