An Adaptive Primal-Dual Subgradient Algorithm for Online Distributed Constrained Optimization

2018 ◽  
Vol 48 (11) ◽  
pp. 3045-3055 ◽  
Author(s):  
Deming Yuan ◽  
Daniel W. C. Ho ◽  
Guo-Ping Jiang
Keyword(s):  
Constrained Optimization ◽  
Primal Dual ◽  
Subgradient Algorithm

scholarly journals Primal–dual algorithm for distributed constrained optimization

2016 ◽  
Vol 96 ◽  
pp. 110-117 ◽  
Author(s):  
Jinlong Lei ◽  
Han-Fu Chen ◽  
Hai-Tao Fang
Keyword(s):  
Constrained Optimization ◽  
Dual Algorithm ◽  
Primal Dual

scholarly journals Box-constrained optimization for minimax supervised learning

2021 ◽  
Vol 71 ◽  
pp. 101-113
Author(s):  
Cyprien Gilet ◽  
Susana Barbosa ◽  
Lionel Fillatre
Keyword(s):  
Constrained Optimization ◽  
Empirical Bayes ◽  
Optimization Procedure ◽  
Affine Function ◽  
Bayes Risk ◽  
Piecewise Affine ◽  
Empirical Risk ◽  
Polyhedral Domain ◽  
Subgradient Algorithm ◽  
Constrained Minimax

In this paper, we present the optimization procedure for computing the discrete boxconstrained minimax classifier introduced in [1, 2]. Our approach processes discrete or beforehand discretized features. A box-constrained region defines some bounds for each class proportion independently. The box-constrained minimax classifier is obtained from the computation of the least favorable prior which maximizes the minimum empirical risk of error over the box-constrained region. After studying the discrete empirical Bayes risk over the probabilistic simplex, we consider a projected subgradient algorithm which computes the prior maximizing this concave multivariate piecewise affine function over a polyhedral domain. The convergence of our algorithm is established.

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