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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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The Surprising Mathematics of Longest Increasing Subsequences
TL;DR: In a surprising sequence of developments, the longest increasing subsequence problem has proven to have deep connections to many seemingly unrelated branches of mathematics, such as random permutations, random matrices, Young tableaux, and the corner growth model as discussed by the authors.
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Dynamic Pricing for Non-Perishable Products with Demand Learning
Victor F. Araman,René Caldentey +1 more
TL;DR: The retailer's problem is formulated as a (Poisson) intensity control problem and the structural properties of an optimal solution are derived, and a simple and efficient approximated solution is suggested.
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An Accelerated Linearized Alternating Direction Method of Multipliers
TL;DR: It is demonstrated that for solving a class of convex composite optimization with linear constraints, the rate of convergence of AADMM is better than that of linearized ADMM, in terms of their dependence on the Lipschitz constant of the smooth component.
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A generalized entropy criterion for Nevanlinna-Pick interpolation with degree constraint
TL;DR: A generalized entropy criterion for solving the rational Nevanlinna-Pick problem for n+1 interpolating conditions and the degree of interpolants bounded by n is presented, which requires a selection of a monic Schur polynomial of degree n.
Kullback-Leibler divergence constrained distributionally robust optimization
Zhaolin Hu,Jeff Liu Hong +1 more
TL;DR: The main contribution of the paper is to show that the KL divergence constrained DRO problems are often of the same complexity as their original stochastic programming problems and, thus, KL divergence appears a good candidate in modeling distribution ambiguities in mathematical programming.
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.