An accelerated proximal gradient algorithm for nuclear norm regularized linear least squares problems

By Kim-Chuan Toh, Sangwoon Yun. 2009

999 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/6d389485b399ae7b60c1f426f1168f4eacaba64f

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Citations in the corpus

Trace Norm Regularization: Reformulations, Algorithms, and Multi-Task Learning (2010, methodology): “1, each iteration requires only one SVD of the n × m matrix Y − 1 L∇fP(Y ); see [14,47].”
Robust Matrix Completion via Joint Schatten p-Norm and lp-Norm Minimization (2012, methodology): “Following [9], given a matrix M created by the aforementioned procedures, we corrupt it by a noise matrix N whose element are i.”
Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm (2012, methodology): “An accelerated proximal gradient algorithm is developed in [33] based on a fast iterative shrinkage-thresholding algorithm [1] for compressive sensing.”
A collaborative framework for 3D alignment and classification of heterogeneous subvolumes in cryo-electron tomography (2010, methodology): “ be directly applied to a relaxed version of the RPCA problem, by identifying X = (A,E), f(X) = 1 µ kD −A − Ek2F , and g(X) = kAk∗ +λkEk1, where µ is a small positive scalar. A continuation technique [19], which varies µ, starting from a large initial value µ0 and decreasing it geometrically with ea”
Matrix Completion from Noisy Entries (2009, background): “A number of iterative schemes to solve the convex optimization problem appeared soon thereafter [6, 7, 8] (also see [9] for a generalization).”
A Sparse Plus Low Rank Maximum Entropy Language Model (2012, methodology): “Our algorithm is a block-coordinate variant of the accelerated proximal gradient descent algorithm introduced by Toh and Yun in [12], modified to alternate between the `1 and ‖·‖∗ regularized terms.”
Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Matrices via Convex Optimization (2009, methodology): “7 In practice, convergence speed is dramatically improved by employing a continuation strategy in which μ starts relatively large and then decreases geometrically at each iteration until reaching a lower bound, μ̄ (as in [21]).”
Fast Convex Optimization Algorithms for Exact Recovery of a Corrupted Low-Rank Matrix (2009, methodology): “1Similar techniques have been applied to the matrix completion problem by [19].”
AdaLoRA: Adaptive Budget Allocation for Parameter-Efficient Fine-Tuning (2023, methodology): “There are some methods to control the rank of matrices in the existing literature of matrix approximation (Cai et al., 2010; Koltchinskii et al., 2011; Toh & Yun, 2010).”
Robust Photometric Stereo via Low-Rank Matrix Completion and Recovery (2010, methodology): “Fortunately, there has been a flurry of work recently on developing scalable algorithms for high-dimensional nuclear-norm minimization [16, 20, 21].”
Large Margin Metric Learning for Multi-Label Prediction (2015, methodology): “To handle many labels, the accelerated proximal gradient (APG) method (Beck and Teboulle 2009; Toh and Yun 2009) is adapted to solve the reduced problem.”