scholarly journals Characterizing robust weak sharp solution sets of convex optimization problems with uncertainty

2020 ◽  
Vol 16 (6) ◽  
pp. 2651-2673
Author(s):  
Jutamas Kerdkaew ◽  
◽  
Rabian Wangkeeree ◽  
Keyword(s):  
Convex Optimization ◽  
Optimization Problems ◽  
Solution Sets ◽  
Convex Optimization Problems ◽  
Weak Sharp Solution ◽  
Weak Sharp

scholarly journals Decentralized and parallel primal and dual accelerated methods for stochastic convex programming problems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Darina Dvinskikh ◽  
Alexander Gasnikov
Keyword(s):  
Convex Optimization ◽  
Inverse Problems ◽  
Convex Programming ◽  
Data Science ◽  
Optimization Problems ◽  
Stochastic Gradient ◽  
Logarithmic Factor ◽  
Accelerated Methods ◽  
Convex Optimization Problems ◽  
Primal And Dual

Abstract We introduce primal and dual stochastic gradient oracle methods for decentralized convex optimization problems. Both for primal and dual oracles, the proposed methods are optimal in terms of the number of communication steps. However, for all classes of the objective, the optimality in terms of the number of oracle calls per node takes place only up to a logarithmic factor and the notion of smoothness. By using mini-batching technique, we show that the proposed methods with stochastic oracle can be additionally parallelized at each node. The considered algorithms can be applied to many data science problems and inverse problems.

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