scholarly journals A new nonmonotone line search technique for unconstrained optimization

2008 ◽  
Vol 219 (1) ◽  
pp. 134-144 ◽  
Author(s):  
Zhensheng Yu ◽  
Dingguo Pu
Keyword(s):  
Unconstrained Optimization ◽  
Line Search ◽  
Nonmonotone Line Search ◽  
Search Technique ◽  
Line Search Technique

A Simulated Annealing-Based Barzilai–Borwein Gradient Method for Unconstrained Optimization Problems

2019 ◽  
Vol 36 (04) ◽  
pp. 1950017 ◽  
Author(s):  
Wen-Li Dong ◽  
Xing Li ◽  
Zheng Peng
Keyword(s):  
Simulated Annealing ◽  
Unconstrained Optimization ◽  
Gradient Method ◽  
Line Search ◽  
High Efficiency ◽  
Optimization Problems ◽  
Search Technique ◽  
Unconstrained Optimization Problems ◽  
Armijo Line Search ◽  
Line Search Technique

In this paper, we propose a simulated annealing-based Barzilai–Borwein (SABB) gradient method for unconstrained optimization problems. The SABB method accepts the Barzilai–Borwein (BB) step by a simulated annealing rule. If the BB step cannot be accepted, the Armijo line search is used. The global convergence of the SABB method is established under some mild conditions. Numerical experiments indicate that, compared to some existing BB methods using nonmonotone line search technique, the SABB method performs well with high efficiency.

scholarly journals THE BARZILAI AND BORWEIN GRADIENT METHOD WITH NONMONOTONE LINE SEARCH FOR NONSMOOTH CONVEX OPTIMIZATION PROBLEMS

2012 ◽  
Vol 17 (2) ◽  
pp. 203-216 ◽  
Author(s):  
Gonglin Yuan ◽  
Zengxin Wei
Keyword(s):  
Line Search ◽  
Optimization Problems ◽  
Nonmonotone Line Search ◽  
Gradient Algorithm ◽  
Search Technique ◽  
Nonsmooth Problems ◽  
Smooth Optimization ◽  
Line Search Technique ◽  
Nonsmooth Convex Minimization ◽  
The Given

The Barzilai and Borwein gradient algorithm has received a great deal of attention in recent decades since it is simple and effective for smooth optimization problems. Whether can it be extended to solve nonsmooth problems? In this paper, we answer this question positively. The Barzilai and Borwein gradient algorithm combined with a nonmonotone line search technique is proposed for nonsmooth convex minimization. The global convergence of the given algorithm is established under suitable conditions. Numerical results show that this method is efficient.

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