Journal ArticleDOI
The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming
TLDR
This method can be regarded as a generalization of the methods discussed in [1–4] and applied to the approximate solution of problems in linear and convex programming.Abstract:
IN this paper we consider an iterative method of finding the common point of convex sets. This method can be regarded as a generalization of the methods discussed in [1–4]. Apart from problems which can be reduced to finding some point of the intersection of convex sets, the method considered can be applied to the approximate solution of problems in linear and convex programming.read more
Citations
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Book
Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers
TL;DR: It is argued that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas.
Proceedings ArticleDOI
Advances in kernel methods: support vector learning
TL;DR: Support vector machines for dynamic reconstruction of a chaotic system, Klaus-Robert Muller et al pairwise classification and support vector machines, Ulrich Kressel.
Journal ArticleDOI
Strictly Proper Scoring Rules, Prediction, and Estimation
TL;DR: The theory of proper scoring rules on general probability spaces is reviewed and developed, and the intuitively appealing interval score is proposed as a utility function in interval estimation that addresses width as well as coverage.
Book
Graphical Models, Exponential Families, and Variational Inference
TL;DR: The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in large-scale statistical models.
Journal ArticleDOI
The Split Bregman Method for L1-Regularized Problems
Tom Goldstein,Stanley Osher +1 more
TL;DR: This paper proposes a “split Bregman” method, which can solve a very broad class of L1-regularized problems, and applies this technique to the Rudin-Osher-Fatemi functional for image denoising and to a compressed sensing problem that arises in magnetic resonance imaging.
References
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Journal ArticleDOI
The Relaxation Method for Linear Inequalities
TL;DR: In various numerical problems one is confronted with the task of solving a system of linear inequalities: (1.1) (i = 1, …,m) assuming, of course, that the above system is consistent as mentioned in this paper.
Journal ArticleDOI
The Relaxation Method for Linear Inequalities
T. S. Motzkin,I. J. Schoenberg +1 more
TL;DR: In this article, a closed set of points in the n-dimensional euclidean space En is considered, and the closest point to the set A is defined as a point p such that there is no point p 1 which is point-wise closer than p to A.
Journal ArticleDOI
A duality theorem for convex programs
TL;DR: A proof is given for a duality theorem for a class of convex programs, i.e., constrained minimization of conveX functions, which is based on the inequality of the following type: For α ≥ 1, β ≥ 1 using LaSalle's inequality.