scholarly journals Global convergence of nonmonotone descent methods for unconstrained optimization problems

2002 ◽  
Vol 146 (1) ◽  
pp. 89-98 ◽  
Author(s):  
Wenyu Sun ◽  
Jiye Han ◽  
Jie Sun
Keyword(s):  
Global Convergence ◽  
Unconstrained Optimization ◽  
Optimization Problems ◽  
Descent Methods ◽  
Unconstrained Optimization Problems

A Non-Monotone Line Search Combination Technique for Unconstrained Optimization

2014 ◽  
Vol 8 (1) ◽  
pp. 218-221 ◽  
Author(s):  
Ping Hu ◽  
Zong-yao Wang
Keyword(s):  
Global Convergence ◽  
Unconstrained Optimization ◽  
Numerical Experiments ◽  
Line Search ◽  
Optimization Problems ◽  
Search Algorithm ◽  
New Combination ◽  
Combination Rule ◽  
Combination Technique ◽  
Unconstrained Optimization Problems

We propose a non-monotone line search combination rule for unconstrained optimization problems, the corresponding non-monotone search algorithm is established and its global convergence can be proved. Finally, we use some numerical experiments to illustrate the new combination of non-monotone search algorithm’s effectiveness.

scholarly journals On q-BFGS algorithm for unconstrained optimization problems

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shashi Kant Mishra ◽  
Geetanjali Panda ◽  
Suvra Kanti Chakraborty ◽  
Mohammad Esmael Samei ◽  
Bhagwat Ram
Keyword(s):  
Global Convergence ◽  
Objective Function ◽  
Unconstrained Optimization ◽  
Optimization Problems ◽  
Objective Function Value ◽  
Numerical Test ◽  
Step Length ◽  
Test Problems ◽  
Bfgs Method ◽  
Unconstrained Optimization Problems

AbstractVariants of the Newton method are very popular for solving unconstrained optimization problems. The study on global convergence of the BFGS method has also made good progress. The q-gradient reduces to its classical version when q approaches 1. In this paper, we propose a quantum-Broyden–Fletcher–Goldfarb–Shanno algorithm where the Hessian is constructed using the q-gradient and descent direction is found at each iteration. The algorithm presented in this paper is implemented by applying the independent parameter q in the Armijo–Wolfe conditions to compute the step length which guarantees that the objective function value decreases. The global convergence is established without the convexity assumption on the objective function. Further, the proposed method is verified by the numerical test problems and the results are depicted through the performance profiles.

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