A nonlinear conjugate gradient method based on the MBFGS secant condition
Authors:
- 16 August 2006
- journal article
- research article
- Published by Taylor & Francis in Optimization Methods and Software
- Vol. 21 (5) , 707-714
Abstract
In this article, a new conjugate gradient method based on the MBFGS secant condition is derived, which is regarded as a modified version of Dai–Liao method or Yabe–Takano method. This method is shown to be globally convergent under some assumptions. It is new feature that the proof of global convergence of this method is very simple without proving so-called Property(∗) given by Gilbert and Nocedal for general unconstrained optimization problems. Our numerical results show that this method is efficient for the given test problems.Keywords
This publication has 12 references indexed in Scilit:
- Global Convergence Properties of Nonlinear Conjugate Gradient Methods with Modified Secant ConditionComputational Optimization and Applications, 2004
- Convergence Properties of the BFGS AlgoritmSIAM Journal on Optimization, 2002
- Properties and numerical performance of quasi-Newton methods with modified quasi-Newton equationsJournal of Computational and Applied Mathematics, 2001
- A modified BFGS method and its global convergence in nonconvex minimizationJournal of Computational and Applied Mathematics, 2001
- New Conjugacy Conditions and Related Nonlinear Conjugate Gradient MethodsApplied Mathematics & Optimization, 2001
- Convergence Properties of Nonlinear Conjugate Gradient MethodsSIAM Journal on Optimization, 2000
- New Quasi-Newton Equation and Related Methods for Unconstrained OptimizationJournal of Optimization Theory and Applications, 1999
- A Nonlinear Conjugate Gradient Method with a Strong Global Convergence PropertySIAM Journal on Optimization, 1999
- Global Convergence Properties of Conjugate Gradient Methods for OptimizationSIAM Journal on Optimization, 1992
- Descent Property and Global Convergence of the Fletcher—Reeves Method with Inexact Line SearchIMA Journal of Numerical Analysis, 1985