scholarly journals A modified scaled memoryless BFGS preconditioned conjugate gradient algorithm for nonsmooth convex optimization

2018 ◽  
Vol 14 (2) ◽  
pp. 785-801
Author(s):  
Yigui Ou ◽  
◽  
Xin Zhou
Keyword(s):  
Convex Optimization ◽  
Conjugate Gradient ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Preconditioned Conjugate Gradient ◽  
Nonsmooth Convex Optimization

scholarly journals Wei-Yao-Liu Conjugate Gradient Algorithm for Nonsmooth Convex Optimization Problems

2020 ◽  
Vol 8 (2) ◽  
pp. 403-413
Author(s):  
Yaping Hu ◽  
Liying Liu ◽  
Yujie Wang
Keyword(s):  
Convex Optimization ◽  
Conjugate Gradient ◽  
Optimization Problems ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Nonsmooth Convex Optimization ◽  
Convex Optimization Problem ◽  
Yosida Regularization ◽  
Global Convergence Property ◽  
Approximate Function

This paper presents a Wei-Yao-Liu conjugate gradient algorithm for nonsmooth convex optimization problem. The proposed algorithm makes use of approximate function and gradient values of the Moreau-Yosida regularization function instead of the corresponding exact values.  Under suitable conditions, the global convergence property could be established for the proposed conjugate gradient  method. Finally, some numerical results are reported to show the efficiency of our algorithm.

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