Journal ArticleDOI
Constrained minimization methods
E.S. Levitin,B.T. Polyak +1 more
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This article is published in Ussr Computational Mathematics and Mathematical Physics.The article was published on 1966-01-01. It has received 785 citations till now.read more
Citations
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A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
Amir Beck,Marc Teboulle +1 more
TL;DR: 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.
Journal ArticleDOI
Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization
TL;DR: L-BFGS-B is a limited-memory algorithm for solving large nonlinear optimization problems subject to simple bounds on the variables, intended for problems in which information on the Hessian matrix is difficult to obtain, or for large dense problems.
Journal ArticleDOI
Signal recovery by proximal forward-backward splitting ∗
TL;DR: It is shown that various inverse problems in signal recovery can be formulated as the generic problem of minimizing the sum of two convex functions with certain regularity properties, which makes it possible to derive existence, uniqueness, characterization, and stability results in a unified and standardized fashion for a large class of apparently disparate problems.
Posted Content
Proximal Splitting Methods in Signal Processing
Abstract: The proximity operator of a convex function is a natural extension of the notion of a projection operator onto a convex set. This tool, which plays a central role in the analysis and the numerical solution of convex optimization problems, has recently been introduced in the arena of signal processing, where it has become increasingly important. In this paper, we review the basic properties of proximity operators which are relevant to signal processing and present optimization methods based on these operators. These proximal splitting methods are shown to capture and extend several well-known algorithms in a unifying framework. Applications of proximal methods in signal recovery and synthesis are discussed.
Book ChapterDOI
Proximal Splitting Methods in Signal Processing
TL;DR: The basic properties of proximity operators which are relevant to signal processing and optimization methods based on these operators are reviewed and proximal splitting methods are shown to capture and extend several well-known algorithms in a unifying framework.
References
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Journal ArticleDOI
The Gradient Projection Method for Nonlinear Programming. Part I. Linear Constraints
TL;DR: The gradient projection method was originally presented to the American Mathematical Society for solving linear programming problems by Dantzig et al. as discussed by the authors, and has been applied to nonlinear programming problems as well.