A new accelerated conjugate gradient method for large-scale unconstrained optimization

Abstract

Abstract In this paper, we present a new conjugate gradient method using an acceleration scheme for solving large-scale unconstrained optimization. The generated search direction satisfies both the sufficient descent condition and the Dai–Liao conjugacy condition independent of line search. Moreover, the value of the parameter contains more useful information without adding more computational cost and storage requirements, which can improve the numerical performance. Under proper assumptions, the global convergence result of the proposed method with a Wolfe line search is established. Numerical experiments show that the given method is competitive for unconstrained optimization problems, with a maximum dimension of 100,000.

Keywords

• Conjugate gradient
• Descent condition
• Dai–Liao conjugacy condition
• Global convergence
• Large-scale unconstrained optimization