scholarly journals Smoothing accelerated algorithm for constrained nonsmooth convex optimization problems

2020 ◽  
Vol 50 (12) ◽  
pp. 1651
Author(s):  
Bian Wei
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.

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