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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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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.
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Probing the Pareto Frontier for Basis Pursuit Solutions
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Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems
Amir Beck,Marc Teboulle +1 more
TL;DR: 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).
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Regulating a monopolist with unknown costs
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TL;DR: In this paper, the authors consider the problem of how to regulate a monopolistic firm whose costs are unknown to the regulator, and derive an optimal regulatory policy for the case in which the regulator does not know the costs of the firm.
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Constrained Consensus and Optimization in Multi-Agent Networks
TL;DR: In this article, the authors present a distributed algorithm that can be used by multiple agents to align their estimates with a particular value over a network with time-varying connectivity.
References
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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.
Pattern Recognition and Machine Learning
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An Algorithm for Vector Quantizer Design
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TL;DR: An efficient and intuitive algorithm is presented for the design of vector quantizers based either on a known probabilistic model or on a long training sequence of data.