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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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Estimate sequence methods: extensions and approximations
TL;DR: A simple, self-contained, and unified framework for the study of estimate sequences is developed, with which some accelerating scheme proposed by Nesterov can be recovered, notably the acceleration procedure for constrained cubic regularization in convex optimization, and obtain easily generalizations to regularization schemes of any order.
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Master Funds in Portfolio Analysis with General Deviation Measures
TL;DR: In this article, generalized measures of deviation are considered as substitutes for standard deviation in a framework like that of classical portfolio theory for coping with the uncertainty inherent in achieving rates of return beyond the risk-free rate.
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Living on the edge: A geometric theory of phase transitions in convex optimization
TL;DR: A new summary parameter, called the statistical dimension, is introduced that canonically extends the dimension of a linear subspace to the class of convex cones and leads to an approximate version of the conic kinematic formula that gives bounds on the probability that a randomly oriented cone shares a ray with a fixed cone.
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An Efficient Inexact Symmetric Gauss-Seidel Based Majorized ADMM for High-Dimensional Convex Composite Conic Programming
TL;DR: The results show that for the vast majority of the tested problems, the sGS-imsPADMM is 2–3 times faster than the directly extended multi-block ADMM with the aggressive step-length of 1.618, which is currently the benchmark among first-order methods for solving multi- block linear and quadratic SDP problems though its convergence is not guaranteed.
Proceedings ArticleDOI
Distributed Non-Autonomous Power Control through Distributed Convex Optimization
TL;DR: This work considers the uplink power control problem where mobile users in different cells are communicating with their base stations and proposes convergent, distributed and iterative power control algorithms that are non- autonomous.