Result: Stochastic Variance Reduced Gradient for Affine Rank Minimization Problem: Stochastic variance reduced gradient for affine rank minimization problem
Title:
Stochastic Variance Reduced Gradient for Affine Rank Minimization Problem: Stochastic variance reduced gradient for affine rank minimization problem
Authors:
Source:
SIAM Journal on Imaging Sciences. 17:1118-1144
Publication Status:
Preprint
Publisher Information:
Society for Industrial & Applied Mathematics (SIAM), 2024.
Publication Year:
2024
Subject Terms:
low-rank matrix, FOS: Computer and information sciences, Convex programming, stochastic variance reduced gradient, Computer Science - Information Theory, Information Theory (cs.IT), 0211 other engineering and technologies, affine rank minimization, Matrix completion problems, 02 engineering and technology, 01 natural sciences, Numerical mathematical programming methods, Optimization and Control (math.OC), 0202 electrical engineering, electronic engineering, information engineering, FOS: Mathematics, 0101 mathematics, Mathematics - Optimization and Control
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
1936-4954
DOI:
10.1137/23m1555387
DOI:
10.48550/arxiv.2211.02802
Access URL:
Rights:
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....f7d9eeec18c2912bb75fd0ab1e0db803
Database:
OpenAIRE
Further Information
We develop an efficient stochastic variance reduced gradient descent algorithm to solve the affine rank minimization problem consists of finding a matrix of minimum rank from linear measurements. The proposed algorithm as a stochastic gradient descent strategy enjoys a more favorable complexity than full gradients. It also reduces the variance of the stochastic gradient at each iteration and accelerate the rate of convergence. We prove that the proposed algorithm converges linearly in expectation to the solution under a restricted isometry condition. The numerical experiments show that the proposed algorithm has a clearly advantageous balance of efficiency, adaptivity, and accuracy compared with other state-of-the-art greedy algorithms.