A New Conjugate Gradient Parameter via Modification of Liu-Storey Formula for Optimization Problem and Image Restoration

Abstract

The conjugate gradient (CG) algorithms are one of the efficient numerical algorithms that are characterized by simplicity and nice convergence properties. However, recent modification of the CG method has complicated algorithms and might fail to converge under certain line search procedures. Also, the performance of some of the classical methods are yet to be tested on real-life application problems. This study presents a new modification of conjugate gradients (CG) algorithm for optimization problems and image restoration. The new formula is a modification of the Liu-Storey (LS) CG formula that generates the descent direction for objective functions. We established the convergence of our formula under suitable line search condition. Results from computational experiments were obtained and they showed that our new approach outperforms other existing algorithms such as Hestenes-Steifel (HS), LS, Dai-Yuan (DY) and Rivaie-Mustafa-Ismail-Leong (RMIL) in terms of both iteration numbers and based on CPU time. To further illustrate the efficiency of our proposed method, the formula was extended to restore images corrupted by impulse noise and the results obtained showed that the method was able to restore images with better accuracy which further confirmed the efficiency and robustness of our method.