An improved spectral CG method based on Dai–Liao conjugacy condition and quasi-Newton direction

In this article, with a convex combination of two conjugate gradient (CG) parameters, a novel improved CG parameter is introduced that leads to a new CG method with more appropriate theoretical and computational properties. The convex combination parameter in our proposed CG parameter is obtained such that the search direction satisfies the Dai–Liao conjugacy condition and aligns with the quasi-Newton direction. Then, the corresponding spectral CG method is formulated, having the property that its generated search direction satisfies the sufficient descent property independent of the line search technique. Under some appropriate assumptions, we establish the global convergence of our method for general non-convex functions. Numerical results on solving unconstrained optimization test problems from the CUTEst collection demonstrate the efficiency of our proposed approach in application. Moreover, we also demonstrate the efficiency of our proposed method in solving image restoration problems.