scholarly journals An Accelerated Hybrid Proximal Extragradient Method for Convex Optimization and Its Implications to Second-Order Methods

2013 ◽  
Vol 23 (2) ◽  
pp. 1092-1125 ◽  
Author(s):  
Renato D. C. Monteiro ◽  
B. F. Svaiter
Keyword(s):  
Convex Optimization ◽  
Extragradient Method ◽  
Second Order ◽  
Hybrid Proximal Extragradient Method ◽  
Second Order Methods

scholarly journals Reachability of optimal convergence rate estimates for high-order numerical convex optimization methods

2019 ◽  
Vol 484 (6) ◽  
pp. 667-671
Author(s):  
A. V. Gasnikov ◽  
E. A. Gorbunov ◽  
D. A. Kovalev ◽  
A. A. M. Mokhammed ◽  
E. A. Chernousova
Keyword(s):  
Convex Optimization ◽  
Convergence Rate ◽  
Optimization Problems ◽  
Extragradient Method ◽  
Auxiliary Problem ◽  
Optimization Methods ◽  
Step Size ◽  
Tensor Method ◽  
Higher Derivatives ◽  
Hybrid Proximal Extragradient Method

The Monteiro-Svaiter accelerated hybrid proximal extragradient method (2013) with one step of Newton’s method used at every iteration for the approximate solution of an auxiliary problem is considered. The Monteiro-Svaiter method is optimal (with respect to the number of gradient and Hessian evaluations for the optimized function) for sufficiently smooth convex optimization problems in the class of methods using only the gradient and Hessian of the optimized function. An optimal tensor method involving higher derivatives is proposed by replacing Newton’s step with a step of Yu.E. Nesterov’s recently proposed tensor method (2018) and by using a special generalization of the step size selection condition in the outer accelerated proximal extragradient method. This tensor method with derivatives up to the third order inclusive is found fairly practical, since the complexity of its iteration is comparable with that of Newton’s one. Thus, a constructive solution is obtained for Nesterov’s problem (2018) of closing the gap between tight lower and overstated upper bounds for the convergence rate of existing tensor methods of order p ≥ 3.

scholarly journals H2 model reduction for diffusively coupled second-order networks by convex-optimization

Automatica ◽  
2022 ◽  
Vol 137 ◽  
pp. 110118
Author(s):  
Lanlin Yu ◽  
Xiaodong Cheng ◽  
Jacquelien M.A. Scherpen ◽  
Junlin Xiong
Keyword(s):  
Convex Optimization ◽  
Model Reduction ◽  
Second Order

scholarly journals Distributed Second-Order Methods With Increasing Number of Working Nodes

2020 ◽  
Vol 65 (2) ◽  
pp. 846-853
Author(s):  
Natasa Krklec Jerinkic ◽  
Dusan Jakovetic ◽  
Natasa Krejic ◽  
Dragana Bajovic
Keyword(s):  
Second Order ◽  
Second Order Methods
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