Gradient-Free Two-Point Methods for Solving Stochastic Nonsmooth Convex Optimization Problems with Small Non-Random Noises

2018 ◽  
pp. 38-49
Author(s):  
Anastasya Bayandina ◽  
◽  
Aleksandr Gasnikov ◽  
Anastasya Lagunovskaya ◽  
◽  
...  
Keyword(s):  
Convex Optimization ◽  
Optimization Problems ◽  
Nonsmooth Convex Optimization ◽  
Convex Optimization Problems

scholarly journals Multivariate Spectral Gradient Algorithm for Nonsmooth Convex Optimization Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Yaping Hu
Keyword(s):  
Convex Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Gradient Algorithm ◽  
Nonsmooth Convex Optimization ◽  
Convex Optimization Problem ◽  
Convex Optimization Problems ◽  
Yosida Regularization ◽  
Approximate Function ◽  
Original Objective

We propose an extended multivariate spectral gradient algorithm to solve the nonsmooth convex optimization problem. First, by using Moreau-Yosida regularization, we convert the original objective function to a continuously differentiable function; then we use approximate function and gradient values of the Moreau-Yosida regularization to substitute the corresponding exact values in the algorithm. The global convergence is proved under suitable assumptions. Numerical experiments are presented to show the effectiveness of this algorithm.

Sign in / Sign up

Export Citation Format

Share Document