论文标题
加速无凝结复合梯度方法，用于非凸光谱优化问题
Accelerated Inexact Composite Gradient Methods for Nonconvex Spectral Optimization Problems
论文作者
论文摘要
本文介绍了两种不精确的复合梯度方法，一种内部加速，另一种是双重加速的，用于求解一类非Convex频谱复合材料优化问题。更具体地说，这些问题的目标函数是$ f_1 + f_2 + h $的形式，其中$ f_1 $和$ f_2 $是与Lipschitz连续梯度的可区分的非convex矩阵函数，$ h $是适当的闭合convex矩阵函数，$ f_2 $和$ h $均表现为在功能上表现为在功能上，可以在运行中，他们在signult octuctation sistuct sistuct sistuct sistuct sistut sistut sistut sistut sistut sistut sistut。该方法实质上使用加速的复合梯度方法来解决涉及$ f_1 $线性近似和$ f_2 $和$ h $的奇异值函数的近端子问题。与其他基于复合梯度的方法不同，所提出的方法利用了目标函数基础的复合和光谱结构，以便有效地生成其溶液。提出了数值实验，以证明这些方法在一组现实世界和随机生成的光谱优化问题上的实用性。
This paper presents two inexact composite gradient methods, one inner accelerated and another doubly accelerated, for solving a class of nonconvex spectral composite optimization problems. More specifically, the objective function for these problems is of the form $f_1 + f_2 + h$ where $f_1$ and $f_2$ are differentiable nonconvex matrix functions with Lipschitz continuous gradients, $h$ is a proper closed convex matrix function, and both $f_2$ and $h$ can be expressed as functions that operate on the singular values of their inputs. The methods essentially use an accelerated composite gradient method to solve a sequence of proximal subproblems involving the linear approximation of $f_1$ and the singular value functions underlying $f_2$ and $h$. Unlike other composite gradient-based methods, the proposed methods take advantage of both the composite and spectral structure underlying the objective function in order to efficiently generate their solutions. Numerical experiments are presented to demonstrate the practicality of these methods on a set of real-world and randomly generated spectral optimization problems.
