A modified PRP conjugate gradient algorithm with nonmonotone line search for nonsmooth convex optimization problems

2015 ◽  
Vol 51 (1-2) ◽  
pp. 397-412 ◽  
Author(s):  
Gonglin Yuan ◽  
Zengxin Wei
Keyword(s):  
Convex Optimization ◽  
Conjugate Gradient ◽  
Line Search ◽  
Optimization Problems ◽  
Conjugate Gradient Algorithm ◽  
Nonmonotone Line Search ◽  
Gradient Algorithm ◽  
Nonsmooth Convex Optimization ◽  
Convex Optimization Problems

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.

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.

scholarly journals A Conjugate Gradient Algorithm under Yuan-Wei-Lu Line Search Technique for Large-Scale Minimization Optimization Models

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Xiangrong Li ◽  
Songhua Wang ◽  
Zhongzhou Jin ◽  
Hongtruong Pham
Keyword(s):  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Search Technique ◽  
Inexact Line Search ◽  
Line Search Technique ◽  
Large Scale Unconstrained Optimization

This paper gives a modified Hestenes and Stiefel (HS) conjugate gradient algorithm under the Yuan-Wei-Lu inexact line search technique for large-scale unconstrained optimization problems, where the proposed algorithm has the following properties: (1) the new search direction possesses not only a sufficient descent property but also a trust region feature; (2) the presented algorithm has global convergence for nonconvex functions; (3) the numerical experiment showed that the new algorithm is more effective than similar algorithms.

Sign in / Sign up

Export Citation Format

Share Document