A Developed Version of Conjugate Gradient Method With a New Parameter for Dai-Liao Conjugacy Condition With an Application to Solar Panel

Conjugate Gradient (CG) methods are broadly employed in solving bigger-scale unconstrained optimization problems. Two famous methods are the Hestenes–Stiefel (HS) as well as Polak–Ribière–Polyak (PRP) CG methods, which usually work well in practice. However, they cannot satisfy the Global Convergence (GC) property. To retain and enhance the previous practical behavior as well as rectify the latter difficulty, this paper constructs a new CG method based on the Dai-Liao conjugacy condition, the Restart Property (RP), and the Lipschitz constant. It is refined that the suggested method meets the sufficient Descent Condition (DC), and the GC properties with the new RP depend on the Lipschitz Constant (LC).  To study the behavior of the method, we compared its performance with that of the useful CG-Descent 6.8 as well as non-negative Dai-Liao methods by applying them to 143 optimization problems that are selected from the CUTEst library. The numerical findings indicate that the newly proposed method surpasses the latter two methods as well as other recently published CG methods in terms of the number of iterations, the number of functions, gradient evaluations as well as the CPU time required to solve the problems. In addition, we present an application of the considered CG methods to the solar panel for dust effect and prevent dust accumulation and optimize module performance.