A spectral Fletcher-Reeves conjugate gradient method with integrated strategy for unconstrained optimization and portfolio selection

Abstract

The spectral conjugate gradient (SCG) technique is highly efficient in addressing large-scale unconstrained optimization challenges. This paper presents a structured SCG approach that combines the Quasi-Newton direction and an extended conjugacy condition. Drawing inspiration from the Fletcher-Reeves conjugate gradient (CG) parameter, this method is tailored to improve the general structure of the CG approach. We rigorously establish the global convergence of the algorithm for general functions, using criteria from a Wolfe-line search. Numerical experiments performed on some unconstrained optimization problems highlight the superiority of this new algorithm over certain CG methods with similar characteristics. In the context of portfolio selection, the proposed method extended to address the problem of stock allocation, ensuring optimized returns while minimizing risks. Empirical evaluations demonstrate the efficiency of the method, demonstrating significant improvements in computational efficiency and optimization outcomes.