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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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Linear and strong convergence of algorithms involving averaged nonexpansive operators
TL;DR: In this paper, the authors introduced regularity notions for averaged nonexpansive operators, combined with regularity notion of their fixed point sets, and obtained linear and strong convergence results for quasicyclic, cyclic, and random iterations.
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Nuclear norm minimization for the planted clique and biclique problems
TL;DR: This work considers the problems of finding a maximum clique in a graph and finding amaximum-edge biclique in a bipartite graph and writes both problems as matrix-rank minimization and then relax them using the nuclear norm.
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Connectivity and Set Tracking of Multi-agent Systems Guided by Multiple Moving Leaders
TL;DR: Distributed multi-agent tracking of a convex set specified by multiple moving leaders with unmeasurable velocities is investigated, and necessary and sufficient conditions are obtained for set input-to-state stability and set integral input- to- state stability for a nonlinear neighbor-based coordination rule with switching directed topologies.
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Learning in games via reinforcement and regularization
TL;DR: This paper extends several properties of exponential learning, including the elimination of dominated strategies, the asymptotic stability of strict Nash equilibria, and the convergence of time-averaged trajectories in zero-sum games with an interior Nash equilibrium.
Journal ArticleDOI
An Adaptive Accelerated Proximal Gradient Method and its Homotopy Continuation for Sparse Optimization
Qihang Lin,Lin Xiao +1 more
TL;DR: An accelerated proximal gradient method is presented for problems where the smooth part of the objective function is also strongly convex, and this method incorporates an efficient line-search procedure, and achieves the optimal iteration complexity for such composite optimization problems.
References
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Deep Learning
TL;DR: Deep learning as mentioned in this paper is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts, and it is used in many applications such as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames.
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Increasing Returns and Long-Run Growth
TL;DR: In this paper, the authors present a fully specified model of long-run growth in which knowledge is assumed to be an input in production that has increasing marginal productivity, which is essentially a competitive equilibrium model with endogenous technological change.
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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
TL;DR: Probability distributions of linear models for regression and classification are given in this article, along with a discussion of combining models and combining models in the context of machine learning and classification.
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An Algorithm for Vector Quantizer Design
Y. Linde,A. Buzo,Robert M. Gray +2 more
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.