Optimization problems pose significant computational challenges in various scientific and engineering fields. This paper proposes a novel hybrid algorithm that combines the global convergence properties of the Steepest Descent (SD) method with the superior convergence rate of the Diagonal Quasi-Newton (DQN) method. The key idea is to initiate the optimization process using the SD method to ensure stable progress towards the minimum and then switch to the DQN method based on a defined switching criterion to accelerate the final convergence. Numerical experiments on a set of standard benchmark problems demonstrate that the proposed hybrid method significantly reduces the computational time compared to using the steepest descent (SD) method, the BFGS method, and some diagonal quasi-Newton methods.
Bidabadi, N. (2026). Combining the steepest descent and a diagonal quasi-Newton method for unconstrained optimization. Journal of Mathematical Modeling, (), -. doi: 10.22124/jmm.2026.33059.3012
MLA
Bidabadi, N. . "Combining the steepest descent and a diagonal quasi-Newton method for unconstrained optimization", Journal of Mathematical Modeling, , , 2026, -. doi: 10.22124/jmm.2026.33059.3012
HARVARD
Bidabadi, N. (2026). 'Combining the steepest descent and a diagonal quasi-Newton method for unconstrained optimization', Journal of Mathematical Modeling, (), pp. -. doi: 10.22124/jmm.2026.33059.3012
CHICAGO
N. Bidabadi, "Combining the steepest descent and a diagonal quasi-Newton method for unconstrained optimization," Journal of Mathematical Modeling, (2026): -, doi: 10.22124/jmm.2026.33059.3012
VANCOUVER
Bidabadi, N. Combining the steepest descent and a diagonal quasi-Newton method for unconstrained optimization. Journal of Mathematical Modeling, 2026; (): -. doi: 10.22124/jmm.2026.33059.3012
)