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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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Credit risk optimization with Conditional Value-at-Risk criterion
TL;DR: This paper examines a new approach for credit risk optimization based on the Conditional Value-at-Risk (CVaR) risk measure, the expected loss exceeding Value- at-Risks, also known as Mean Excess, Mean Shortfall, or Tail VaR.
Journal ArticleDOI
Interior Gradient and Proximal Methods for Convex and Conic Optimization
Alfred Auslender,Marc Teboulle +1 more
TL;DR: A class of interior gradient algorithms is derived which exhibits an $O(k^{-2})$ global convergence rate estimate and is illustrated with many applications and examples, including some new explicit and simple algorithms for conic optimization problems.
Journal ArticleDOI
An efficient dynamic auction for heterogeneous commodities
TL;DR: In this article, the authors proposed a new dynamic design for auctioning multiple heterogeneous commodities, generalizing earlier work that treated identical objects, where bidders, rather than being required to behave as price-takers, are permitted to strategically exercise their market power.
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Characterizations of the ranges of some nonlinear operators and applications to boundary value problems
Haim Brezis,Louis Nirenberg +1 more
TL;DR: In this article, the authors implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.php).
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Partially finite convex programming, Part I: Quasi relative interiors and duality theory
TL;DR: The notion of the quasi relative interior of a convex set, an extension of the relative interior in finite dimensions, is developed and used in a constraint qualification for a fundamental Fenchel duality result.
References
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Deep Learning
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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.