Distributed Stochastic Nonconvex Optimization and Learning based on Successive Convex Approximation

一种凸-非凸框架用于增强最小化诱导惩罚

A Convex-Nonconvex Framework for Enhancing Minimization Induced Penalties

本文提出一种凸-非凸框架，通过广义Moreau增强最小化诱导惩罚，在保持整体凸性的同时增强信号分量，并给出收敛算法与数值验证。

Convex and Nonconvex Optimization Are Both Minimax-Optimal for Noisy Blind Deconvolution under Random Designs

We investigate the effectiveness of convex relaxation and nonconvex optimization in solving bilinear systems of equations under two different designs (i.e.$~$a sort of random Fourier design and Gaussian design). Despite the wide applicability, the theoretical understanding about these two paradigms remains largely inadequate in the presence of random noise. The current paper makes two contributions by demonstrating that: (1) a two-stage nonconvex algorithm attains minimax-optimal accuracy within a logarithmic number of iterations. (2) convex relaxation also achieves minimax-optimal statistical…

Bridging Convex and Nonconvex Optimization in Robust PCA: Noise, Outliers, and Missing Data

This paper delivers improved theoretical guarantees for the convex programming approach in low-rank matrix estimation, in the presence of (1) random noise, (2) gross sparse outliers, and (3) missing data. This problem, often dubbed as robust principal component analysis (robust PCA), finds applications in various domains. Despite the wide applicability of convex relaxation, the available statistical support (particularly the stability analysis vis-à-vis random noise) remains highly suboptimal, which we strengthen in this paper. When the unknown matrix is well-conditioned, incoherent, and of co…

波束成形的二十五年进展：从凸与非凸优化到学习技术

Twenty-Five Years of Advances in Beamforming: From Convex and Nonconvex Optimization to Learning Techniques

本文回顾了过去二十五年波束成形从凸优化到非凸优化再到机器学习方法的发展历程，并概述其在多种收发架构、传播环境及传统与新兴应用中的进展。