A survey on the Dai–Liao family of nonlinear conjugate gradient methods

At the beginning of this century, which is characterized by huge flows emerging data, Dai and Liao proposed a pervasive conjugacy condition that triggered interest many optimization scholars. Recognized as sophisticated conjugate gradient (CG) algorithm after about two decades, here we share our visions thoughts on method in framework review study. In regard, first discuss modified Dai–Liao methods based secant equations given literature, mostly with aim applying objective function values addition to information. Then, several adaptive, sort optimal choices for parameter are studied. Especially, devote part study versions Hager–Zhang Dai–Kou CG algorithms, being well-known members class methods. Extensions classical approach also reviewed. Finally, models practical disciplines have been addressed approach, including nonlinear systems equations, image restoration compressed sensing.