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A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
TLDR
A new fast iterative shrinkage-thresholding algorithm (FISTA) which preserves the computational simplicity of ISTA but with a global rate of convergence which is proven to be significantly better, both theoretically and practically. Expand
Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems
  • A. Beck, M. Teboulle
  • Mathematics, Medicine
  • IEEE Transactions on Image Processing
  • 1 November 2009
TLDR
A fast algorithm is derived for the constrained TV-based image deblurring problem with box constraints by combining an acceleration of the well known dual approach to the denoising problem with a novel monotone version of a fast iterative shrinkage/thresholding algorithm (FISTA). Expand
Proximal alternating linearized minimization for nonconvex and nonsmooth problems
TLDR
A self-contained convergence analysis framework is derived and it is established that each bounded sequence generated by PALM globally converges to a critical point. Expand
Mirror descent and nonlinear projected subgradient methods for convex optimization
TLDR
It is shown that the MDA can be viewed as a nonlinear projected-subgradient type method, derived from using a general distance-like function instead of the usual Euclidean squared distance, and derived in a simple way convergence and efficiency estimates. Expand
An Old-New Concept of Convex Risk Measures: The Optimized Certainty Equivalent
The optimized certainty equivalent (OCE) is a decision theoretic criterion based on a utility function, that was first introduced by the authors in 1986. This paper re-examines this fundamentalExpand
Interior Gradient and Proximal Methods for Convex and Conic Optimization
TLDR
A class of interior gradient algorithms is derived which exhibits an $O(k^{-2})$ global convergence rate estimate and is illustrated with many applications and examples, including some new explicit and simple algorithms for conic optimization problems. Expand
A Descent Lemma Beyond Lipschitz Gradient Continuity: First-Order Methods Revisited and Applications
TLDR
A framework which allows to circumvent the intricate question of Lipschitz continuity of gradients by using an elegant and easy to check convexity condition which captures the geometry of the constraints is introduced. Expand
A proximal-based decomposition method for convex minimization problems
TLDR
This paper presents a decomposition method for solving convex minimization problems that preserves the good features of the proximal method of multipliers, with the additional advantage that it leads to a decoupling of the constraints, and is thus suitable for parallel implementation. Expand
Convergence Analysis of a Proximal-Like Minimization Algorithm Using Bregman Functions
An alternative convergence proof of a proximal-like minimization algorithm using Bregman functions, recently proposed by Censor and Zenios, is presented. The analysis allows the establishment of aExpand
Asymptotic cones and functions in optimization and variational inequalities
Convex Analysis and Set Valued Maps: A Review.- Asymptotic Cones and Functions.- Existence and Stability in Optimization Problems.- Minimizing and Stationary Sequences.- Duality in OptimizationExpand
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