A general solution to least squares problems with box constraints and its applications
type: Item
instance of: scholarly article
title: A general solution to least squares problems with box constraints and its applications
zbMATH Open document ID: 1400.65033
DOI: 10.1155/2016/3934872
author: Yueyang Teng
author: Shouliang Qi
author: Dayu Xiao
author: Lisheng Xu
author: Yan Kang
author: Jianhua Li
published in: Mathematical Problems in Engineering
publication date: 2018-10-12T00:00:00Z
review text: Summary: The main contribution of this paper is presenting a flexible solution to the box-constrained least squares problems. This solution is applicable to many existing problems, such as nonnegative matrix factorization, support vector machine, signal deconvolution, and computed tomography reconstruction. The key concept of the proposed algorithm is to replace the minimization of the cost function at each iteration by the minimization of a surrogate, leading to a guaranteed decrease in the cost function. In addition to the monotonicity, the proposed algorithm also owns a few good features including the self-constraint in the feasible region and the absence of a predetermined step size. This paper theoretically proves the global convergence for a special case of below-bounded constraints. Using the proposed mechanism, some valuable algorithms can be derived. The simulation results demonstrate that the proposed algorithm provides performance that is comparable to that of other commonly used methods in numerical experiment and computed tomography reconstruction.
Mathematics Subject Classification ID: 65K10
zbMATH DE Number: 6953133
Wikidata QID: Q59131212
describes a project that uses: D-ADMM
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/3934872
OpenAlex ID: W2432892838
cites work: Bayesian regularization and nonnegative deconvolution for room impulse response estimation
cites work: 10.1162/15324430152748218
cites work: Projected Landweber method and preconditioning
cites work: A general method to devise maximum-likelihood signal restoration multiplicative algorithms with non-negativity constraints.
cites work: Penalized maximum likelihood image restoration with positivity constraints: multiplicative algorithms
cites work: Q5591247
cites work: On the convergence properties of the EM algorithm
cites work: A convergent non-negative deconvolution algorithm with Tikhonov regularization
cites work: Q4060241
cites work: Q3843144
cites work: Improved solution for ill-posed linear systems using a constrained optimization ruled by a penalty: evaluation in nuclear medicine tomography
cites work: A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
cites work: Q4850052
cites work: Q4125663
cites work: Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
cites work: D-ADMM: A Communication-Efficient Distributed Algorithm for Separable Optimization
cites work: Q5689624
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description: scientific article; zbMATH DE number 6953133