Two sufficient descent spectral conjugate gradient algorithms for unconstrained optimization with application

This study introduces a new modification of the conjugate gradient (CG) method (IMRMIL). Additionally, two spectral CG algorithms (SCG1 and SCG2) are constructed for unconstrained optimization functions with practical applications. Unlike the modified search methods, the search directions in these algorithms satisfy the important descent property without imposing additional restrictions and are independent of the line search. The global convergence of the new algorithms is established under suitable Wolfe line search conditions by assuming that the gradient g(x) of a continuously differentiable function f is Lipschitz continuous. Numerical computations on both optimization functions and image restoration problems demonstrate the effectiveness of the proposed algorithms.