Convergence of Liu-storey Conjugate Method with Nonmonotone Armijo Line Search
نویسندگان
چکیده
In this paper, we develop a new nonmonotone Armijo-type line search for LS (Liu-Storey) conjugate gradient method for minimizing functions having Lipschitz continuous partial derivatives. The nonmonotone line search can guarantee the global convergence of original LS method under some mild conditions. AMS Subject Classification: 90C30, 65K05
منابع مشابه
A new class of Conjugate Gradient Methods with extended Nonmonotone Line Search
In this paper, we propose a new nonlinear conjugate gradient method for large-scale unconstrain optimization which possesses the following properties:(i)the sufficient descent condition −g k dk ≥ 7 8 ‖gk‖ 2 holds without any line searches;(ii)With exact line search, this method reduces to a nonlinear version of the Liu-Storey conjugate gradient scheme.(iii)Under some assumption, global converge...
متن کاملGlobal Convergence of a Modified Liu-storey Conjugate Gradient Method
In this paper, we make a modification to the LS conjugate gradient method and propose a descent LS method. The method can generates sufficient descent direction for the objective function. We prove that the method is globally convergent with an Armijo-type line search. Moreover, under mild conditions, we show that the method is globally convergent if the Armijo line search or the Wolfe line sea...
متن کاملA New Hybrid Conjugate Gradient Method Based on Eigenvalue Analysis for Unconstrained Optimization Problems
In this paper, two extended three-term conjugate gradient methods based on the Liu-Storey ({tt LS}) conjugate gradient method are presented to solve unconstrained optimization problems. A remarkable property of the proposed methods is that the search direction always satisfies the sufficient descent condition independent of line search method, based on eigenvalue analysis. The globa...
متن کاملOn efficiency of nonmonotone Armijo-type line searches
Abstract Monotonicity and nonmonotonicity play a key role in studying the global convergence and the efficiency of iterative schemes employed in the field of nonlinear optimization, where globally convergent and computationally efficient schemes are explored. This paper addresses some features of descent schemes and the motivation behind nonmonotone strategies and investigates the efficiency of...
متن کاملA class of nonmonotone Armijo-type line search method for unconstrained optimization
This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date...
متن کامل