Optimization & Operations Research
Nabil Sellami; Romaissa Mellal; Basim A. Hassan
Abstract
This paper introduces two hybrid nonlinear conjugate gradient algorithms, NRB1 and NRB2, for solving unconstrained optimization problems. Both methods are constructed as a convex combination of the AlBayati–AlAssady (BA) and Conjugate Descent methods (CD). The first variant, denoted NRB1, employs ...
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This paper introduces two hybrid nonlinear conjugate gradient algorithms, NRB1 and NRB2, for solving unconstrained optimization problems. Both methods are constructed as a convex combination of the AlBayati–AlAssady (BA) and Conjugate Descent methods (CD). The first variant, denoted NRB1, employs an adaptive combination parameter designed to align its search direction more closely with Newton’s method, improving curvature approximation and acceleration of convergence. The second variant, NRB2, independently satisfies the conjugacy condition without relying on line search mechanisms, enhancing numerical stability. Both methods guarantee sufficient descent and global convergence properties under the strong Wolfe line search criteria. Extensive numerical experiments, using the performance profile of Dolan and Moré, demonstrate that NRB1 and NRB2 consistently outperform some classical conjugate gradient methods, including BA, CD, and Dai–Yuan, particularly for large-scale problems. Furthermore, NRB1 is applied to image restoration under salt-and-pepper noise, achieving competitive or superior peak signal-to-noise ratios (PSNR) compared to the Fletcher–Reeves (FR) algorithm with significantly fewer iterations, especially at high noise intensities.
