Dai-Kou type conjugate gradient methods with a line search only using gradient

Abstract

Abstract In this paper, the Dai-Kou type conjugate gradient methods are developed to solve the optimality condition of an unconstrained optimization, they only utilize gradient information and have broader application scope. Under suitable conditions, the developed methods are globally convergent. Numerical tests and comparisons with the PRP+ conjugate gradient method only using gradient show that the methods are efficient.

Keywords

• conjugate gradient
• optimality condition
• line search
• sufficient descent condition
• global convergence