Globally convergent Dai–Liao conjugate gradient method using quasi-Newton update for unconstrained optimization

Using quasi-Newton update and acceleration scheme, a new Dai–Liao conjugate gradient method that does not need computing or storing any approximate Hessian matrix of the objective function is developed for unconstrained optimization. It is shown that the search direction derived from a modified Perry matrix not only possesses sufficient descent condition but also fulfills Dai–Liao conjugacy condition at each iteration. Under certain assumptions, we establish the global convergence of the proposed method for uniformly convex function and general function, respectively. The numerical results illustrate that the presented method can effectively improve the numerical performance and successfully solve the test problems with a maximum dimension of $100000$.

Keywords

conjugate gradient, unconstrained optimization, sufficient descent, conjugacy condition, global convergence

2010 Mathematics Subject Classification

65K05, 90C06, 90C30

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Received 7 April 2021

Received revised 16 March 2022

Accepted 29 May 2022

Published 27 December 2022