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EXTRA: An Exact First-Order Algorithm for Decentralized Consensus Optimization
TLDR
A novel decentralized exact first-order algorithm (abbreviated as EXTRA) to solve the consensus optimization problem and uses a fixed, large step size, which can be determined independently of the network size or topology.
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A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
TLDR
An alternating minimization algorithm for recovering images from blurry and noisy observations with total variation (TV) regularization from a new half-quadratic model applicable to not only the anisotropic but also the isotropic forms of TV discretizations is proposed.
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Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm
TLDR
A low-rank factorization model is proposed and a nonlinear successive over-relaxation (SOR) algorithm is constructed that only requires solving a linear least squares problem per iteration to improve the capacity of solving large-scale problems.
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A Block Coordinate Descent Method for Regularized Multiconvex Optimization with Applications to Nonnegative Tensor Factorization and Completion
TLDR
This paper considers regularized block multiconvex optimization, where the feasible set and objective function are generally nonconvex but convex in each block of variables and proposes a generalized block coordinate descent method.
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A feasible method for optimization with orthogonality constraints
TLDR
The Cayley transform is applied—a Crank-Nicolson-like update scheme—to preserve the constraints and based on it, curvilinear search algorithms with lower flops are developed with high efficiency for polynomial optimization, nearest correlation matrix estimation and extreme eigenvalue problems.
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Iteratively reweighted algorithms for compressive sensing
  • R. ChartrandW. Yin
  • Computer Science
    IEEE International Conference on Acoustics…
  • 12 May 2008
TLDR
A particular regularization strategy is found to greatly improve the ability of a reweighted least-squares algorithm to recover sparse signals, with exact recovery being observed for signals that are much less sparse than required by an unregularized version.
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An Iterative Regularization Method for Total Variation-Based Image Restoration
We introduce a new iterative regularization procedure for inverse problems based on the use of Bregman distances, with particular focus on problems arising in image processing. We are motivated by…
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On the Linear Convergence of the ADMM in Decentralized Consensus Optimization
TLDR
This paper establishes its linear convergence rate for the decentralized consensus optimization problem with strongly convex local objective functions in terms of the network topology, the properties ofLocal objective functions, and the algorithm parameter.
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An efficient augmented Lagrangian method with applications to total variation minimization
TLDR
An algorithm for solving a class of equality-constrained non-smooth optimization problems (chiefly but not necessarily convex programs) with a particular structure that effectively combines an alternating direction technique with a nonmonotone line search to minimize the augmented Lagrangian function at each iteration is proposed.
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Total variation models for variable lighting face recognition
TLDR
The logarithmic total variation (LTV) model is presented, which has the ability to factorize a single face image and obtain the illumination invariant facial structure, which is then used for face recognition.
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