A hybrid IFR-IDY conjugate gradient algorithm for unconstrained optimization and its application in portfolio selection

This study introduces the Improved Fletcher-Reeves (IFR)-Improved Dai-Yuan (IDY) hybrid conjugate gradient method, which combines the strengths of the IFR and IDY parameters through a minimum-operator strategy to enhance robustness in unconstrained optimization. The method is shown to satisfy descent and global convergence properties under the strong Wolfe line search. Numerical experiments on 134 benchmark functions demonstrate that IFR-IDY achieves superior performance, solving 98 problems more than IFR and IDY and exhibiting faster CPU times and fewer iterations in most cases. The method is also used to solve an IDX30 portfolio optimization problem, which results in an optimal allocation with an expected return of 0.00042 and a risk of 0.000050545. These results highlight the efficiency of IFR-IDY and its practical applicability in real-world decision-making.