An unconstrained optimization method using nonmonotone second order Goldstein’s line search

2007 ◽  
Vol 50 (10) ◽  
pp. 1389-1400 ◽  
Author(s):  
Wen-yu Sun ◽  
Qun-yan Zhou
Keyword(s):  
Unconstrained Optimization ◽  
Line Search ◽  
Optimization Method ◽  
Second Order

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 An algorithm for LC1 optimization

2005 ◽  
Vol 15 (2) ◽  
pp. 301-306 ◽  
Author(s):  
Nada Djuranovic-Milicic
Keyword(s):  
Rate Of Convergence ◽  
Unconstrained Optimization ◽  
Optimization Problems ◽  
Directional Derivative ◽  
Second Order ◽  
General Algorithm ◽  
Unconstrained Optimization Problems ◽  
Convergence Proof

In this paper an algorithm for LC1 unconstrained optimization problems, which uses the second order Dini upper directional derivative is considered. The purpose of the paper is to establish general algorithm hypotheses under which convergence occurs to optimal points. A convergence proof is given, as well as an estimate of the rate of convergence.

scholarly journals A nonmonotone modified BFGS algorithm for nonconvex unconstrained optimization problems

Filomat ◽  
2016 ◽  
Vol 30 (5) ◽  
pp. 1283-1296
Author(s):  
Keyvan Amini ◽  
Somayeh Bahrami ◽  
Shadi Amiri
Keyword(s):  
Unconstrained Optimization ◽  
Line Search ◽  
Optimization Problems ◽  
Hessian Matrix ◽  
Convergence Properties ◽  
Convexity Assumption ◽  
Unconstrained Optimization Problems ◽  
Secant Condition ◽  
Approximate Hessian ◽  
Modified Secant Condition

In this paper, a modified BFGS algorithm is proposed to solve unconstrained optimization problems. First, based on a modified secant condition, an update formula is recommended to approximate Hessian matrix. Then thanks to the remarkable nonmonotone line search properties, an appropriate nonmonotone idea is employed. Under some mild conditions, the global convergence properties of the algorithm are established without convexity assumption on the objective function. Preliminary numerical experiments are also reported which indicate the promising behavior of the new algorithm.

scholarly journals A Dai-Liao Hybrid Hestenes-Stiefel and Fletcher-Revees Methods for Unconstrained Optimization

2021 ◽  
Vol 2 (1) ◽  
pp. 33
Author(s):  
Nasiru Salihu ◽  
Mathew Remilekun Odekunle ◽  
Also Mohammed Saleh ◽  
Suraj Salihu
Keyword(s):  
Unconstrained Optimization ◽  
Line Search ◽  
Optimization Problems ◽  
Convex Combination ◽  
Gradient Methods ◽  
Approximate Solutions ◽  
Step Size ◽  
Conjugacy Condition ◽  
Inexact Line Search ◽  
Wolfe Line Search

Some problems have no analytical solution or too difficult to solve by scientists, engineers, and mathematicians, so the development of numerical methods to obtain approximate solutions became necessary. Gradient methods are more efficient when the function to be minimized continuously in its first derivative. Therefore, this article presents a new hybrid Conjugate Gradient (CG) method to solve unconstrained optimization problems. The method requires the first-order derivatives but overcomes the steepest descent method’s shortcoming of slow convergence and needs not to save or compute the second-order derivatives needed by the Newton method. The CG update parameter is suggested from the Dai-Liao conjugacy condition as a convex combination of Hestenes-Stiefel and Fletcher-Revees algorithms by employing an optimal modulating choice parameterto avoid matrix storage. Numerical computation adopts an inexact line search to obtain the step-size that generates a decent property, showing that the algorithm is robust and efficient. The scheme converges globally under Wolfe line search, and it’s like is suitable in compressive sensing problems and M-tensor systems.

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