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Sparse Approximations with Interior Point Methods
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DOI：10.1137/21M1401103.png)
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摘要
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Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well-conditioned problems. In this paper, specialized variants of an interior point-proximal method of multipliers are proposed and analyzed for problems of this class. Computational experience on a variety of problems, namely, multiperiod portfolio optimization, classification of data coming from functional magnetic resonance imaging, restoration of images corrupted by Poisson noise, and classification via regularized logistic regression, provides substantial evidence that interior point methods, equipped with suitable linear algebra, can offer a noticeable advantage over first-order approaches.
Keyword:
sparse approximations
interior point methods
proximal methods of multipliers
nonlinear convex programming
solution of KKT systems
portfolio optimization
image restoration
classification in machine learning
期刊
IF:
6.1
论文数:
888
被引数:
1.2W
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