Skip to main content

LUP Student Papers

LUND UNIVERSITY LIBRARIES

On Low Rank Recovery Problems Using Quadratic Envelope Regularization

Liu, Qian LU (2024) In Master’s Theses in Mathematical Sciences MATM03 20232
Mathematics (Faculty of Sciences)
Centre for Mathematical Sciences
Abstract
Many optimization models from practical problems are too bad to be worked by standard optimization techniques. Here the bad properties include nonconvexity and high discontinuity, such as the problem named low-rank recovery. The traditional approach, nuclear norm minimization, can solve the low-rank recovery but may contain bias. Algorithms like the FBS and the ADMM are highly effective in convex optimization but may encounter difficulties or fail when applied to nonconvex problems. Inspired by the lower semi-continuous convex envelope, we develop an unbiased approach with the quadratic envelope as a regularizer for the low-rank recovery. By adjusting the parameter value of the regularizer for the different problems, it can be a powerful... (More)
Many optimization models from practical problems are too bad to be worked by standard optimization techniques. Here the bad properties include nonconvexity and high discontinuity, such as the problem named low-rank recovery. The traditional approach, nuclear norm minimization, can solve the low-rank recovery but may contain bias. Algorithms like the FBS and the ADMM are highly effective in convex optimization but may encounter difficulties or fail when applied to nonconvex problems. Inspired by the lower semi-continuous convex envelope, we develop an unbiased approach with the quadratic envelope as a regularizer for the low-rank recovery. By adjusting the parameter value of the regularizer for the different problems, it can be a powerful tool and offer an increased probability for algorithms to converge to the global minima. (Less)
Please use this url to cite or link to this publication:
author
Liu, Qian LU
supervisor
organization
course
MATM03 20232
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Optimization, Non-convex Optimization, Low-rank Recovery, Convex Envelope, Quadratic Envelope
publication/series
Master’s Theses in Mathematical Sciences
report number
LUNFMA-3145-2024
ISSN
1404-6342
other publication id
2024:E2
language
English
id
9144464
date added to LUP
2025-07-01 08:28:16
date last changed
2025-07-01 08:28:16
@misc{9144464,
  abstract     = {{Many optimization models from practical problems are too bad to be worked by standard optimization techniques. Here the bad properties include nonconvexity and high discontinuity, such as the problem named low-rank recovery. The traditional approach, nuclear norm minimization, can solve the low-rank recovery but may contain bias. Algorithms like the FBS and the ADMM are highly effective in convex optimization but may encounter difficulties or fail when applied to nonconvex problems. Inspired by the lower semi-continuous convex envelope, we develop an unbiased approach with the quadratic envelope as a regularizer for the low-rank recovery. By adjusting the parameter value of the regularizer for the different problems, it can be a powerful tool and offer an increased probability for algorithms to converge to the global minima.}},
  author       = {{Liu, Qian}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master’s Theses in Mathematical Sciences}},
  title        = {{On Low Rank Recovery Problems Using Quadratic Envelope Regularization}},
  year         = {{2024}},
}