Quasi — Subgradient algorithms for calculating surrogate constraints

2005 ◽  
pp. 203-236 ◽  
Author(s):  
Jarosław Sikorski
Keyword(s):  
Surrogate Constraints ◽  
Subgradient Algorithms

scholarly journals Distributed Constrained Stochastic Subgradient Algorithms Based on Random Projection and Asynchronous Broadcast over Networks

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
Junlong Zhu ◽  
Ping Xie ◽  
Qingtao Wu ◽  
Mingchuan Zhang ◽  
Ruijuan Zheng ◽  
...  
Keyword(s):  
Information Exchange ◽  
Optimal Solution ◽  
Random Projection ◽  
Learning Rate ◽  
Time Varying ◽  
Optimal Value ◽  
Constraint Set ◽  
Time Varying Networks ◽  
Subgradient Algorithms ◽  
Asymptotic Upper Bound

We consider a distributed constrained optimization problem over a time-varying network, where each agent only knows its own cost functions and its constraint set. However, the local constraint set may not be known in advance or consists of huge number of components in some applications. To deal with such cases, we propose a distributed stochastic subgradient algorithm over time-varying networks, where the estimate of each agent projects onto its constraint set by using random projection technique and the implement of information exchange between agents by employing asynchronous broadcast communication protocol. We show that our proposed algorithm is convergent with probability 1 by choosing suitable learning rate. For constant learning rate, we obtain an error bound, which is defined as the expected distance between the estimates of agent and the optimal solution. We also establish an asymptotic upper bound between the global objective function value at the average of the estimates and the optimal value.

String-averaging incremental stochastic subgradient algorithms

2018 ◽  
Vol 34 (3) ◽  
pp. 665-692
Author(s):  
R. M. Oliveira ◽  
E. S. Helou ◽  
E. F. Costa
Keyword(s):  
Subgradient Algorithms

scholarly journals Dual subgradient algorithms for large-scale nonsmooth learning problems

2013 ◽  
Vol 148 (1-2) ◽  
pp. 143-180 ◽  
Author(s):  
Bruce Cox ◽  
Anatoli Juditsky ◽  
Arkadi Nemirovski
Keyword(s):  
Large Scale ◽  
Learning Problems ◽  
Subgradient Algorithms

scholarly journals Subgradient algorithms for solving variable inequalities

2014 ◽  
Vol 247 ◽  
pp. 1052-1063
Author(s):  
J.Y. Bello Cruz ◽  
G. Bouza Allende ◽  
L.R. Lucambio Pérez
Keyword(s):  
Subgradient Algorithms
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