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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.

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Deep Learning

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Increasing Returns and Long-Run Growth

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Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers

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An Algorithm for Vector Quantizer Design

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On Computation of Generalized Derivatives of the Normal-Cone Mapping and their Applications

TL;DR: A characterization of the isolated calmness property of the mentioned solution map is obtained and strong stationarity conditions for an MPEC with control constraints are derived.
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Safe Certificate-Based Maneuvers for Teams of Quadrotors Using Differential Flatness

TL;DR: The proposed collision avoidance strategy complements existing flight control and planning algorithms by providing trajectory modifications with provable safety guarantees, supported both by the theoretical results and experimental validation on a team of five quadrotors.
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Mesh shape-quality optimization using the inverse mean-ratio metric

TL;DR: A nonlinear fractional program that relocates the vertex coordinates of a given mesh to optimize the average element shape quality as measured by the inverse mean-ratio metric and shows that the block Jacobi preconditioner is positive definite.
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Optimization with Multivariate Conditional Value-at-Risk Constraints

TL;DR: This work focuses on the widely applied risk measure conditional value-at-risk (CVaR), introduces a multivariate CVaR relation, and develops a novel optimization model with multivariatecvaR constraints based on polyhedral scalarization.
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Bandit Learning in Concave N-Person Games

TL;DR: This paper examines the long-run behavior of learning with bandit feedback in non-cooperative concave games and derives an upper bound for the convergence rate of the process that nearly matches the best attainable rate for single-agent bandit stochastic optimization.