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Convex Analysisの二,三の進展について
徹 丸山
- Vol. 70, Iss: 1, pp 97-119
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The article was published on 1977-02-01 and is currently open access. It has received 5933 citations till now.read more
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References
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A Study in the BV Space of a Denoising—Deblurring Variational Problem
TL;DR: In this article, a variational problem arising in image recovery was studied in the framework of functions of bounded variation, and the existence and uniqueness of a solution were proved using lower semicontinuity results for convex functionals of measures.
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On the behavior of information theoretic criteria for model order selection
A.P. Liavas,Phillip A. Regalia +1 more
TL;DR: It is shown that when the noise eigenvalues are not clustered sufficiently closely, then the AIC and the MDL may lead to overmodeling by ignoring an arbitrarily large gap between the signal and the noise Eigenvalues.
Proceedings Article
The non-convex Burer-Monteiro approach works on smooth semidefinite programs
TL;DR: In this article, the authors consider a class of SDP's which includes applications such as max-cut, community detection in the stochastic block model, robust PCA, phase retrieval and synchronization of rotations, and show that the low-rank Burer-Monteiro formulation almost never has any spurious local optima.
Journal ArticleDOI
Absolute value programming
TL;DR: This work investigates equations, inequalities and mathematical programs involving absolute values of variables such as the equation Ax+B|x| = b and shows that this absolute value equation is NP-hard to solve, and that solving it with B = I solves the general linear complementarity problem.
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On Fréchet Subdifferentials
TL;DR: A survey of Fréchet subdifferentiation can be found in this article, where the authors discuss fuzzy results in terms of simple subdifferentials calculated at some points arbitrarily close to the point under consideration.