Control and Optimization, Numerical Analysis, Applied Mathematics
15
Scopus Publications
Scopus Publications
A generalized self-regular Kernel function for large-scale nonlinear optimization problems Mounia Laouar, , Mahmoud Brahimi, Raouf Ziadi, Mohammed A. Saleh, Abdulgader Z. Almaymuni, Benmessaoud Chahinez, , , and Aims Mathematics, 2026 This work investigated the computational efficiency of primal-dual interior-point methods for nonlinear convex optimization by refining both the underlying kernel functions and the barrier parameter update mechanisms. We introduced a unified parametric class of self-regular kernels that generalizes several established barrier families while maintaining optimal theoretical iteration complexity. To bridge the gap between theoretical convergence and practical performance, we proposed an adaptive update rule for the barrier parameter and evaluated various heuristics for its dynamic selection. Extensive numerical testing on a diverse benchmark suite demonstrated that the proposed framework significantly outperforms the Interior Point OPTimizer (IPOPT) solver while maintaining high numerical accuracy and minimal stationarity residuals. Moreover, the framework exhibited robust performance even on nonconvex problems, highlighting its practical versatility beyond the theoretical convex setting.
A Combination of Two Conjugate Gradient Methods Under A New Line Search with its Application in Image Restoration Problems Asma Maiza, Raouf Ziadi, Mohammed A. Saleh, Abdulgader Z. Almaymuni International Journal of Applied Mathematics and Computer Science, 2025 A combined conjugate gradient algorithm is introduced for solving unconstrained optimization problems. In the suggested approach, the conjugate gradient parameter is defined as a combination of PRP (Polak-Ribíere-Polyak) and BRB (Rahali-Belloufi-Benzine) conjugate gradient parameters. To improve the convergence properties, we have adopted a new inexact line search technique that fits in with the suggested approach. The proposed line search technique can be useful for other gradient descent methods. We have established the existence of a step length that meets the new line search conditions. The generated descent direction and the convergence properties of the suggested approach are studied under the new line search conditions and the proposed method converges globally under mild assumptions. Our approach is evaluated on various test functions, and a comparison with similar recent algorithms is carried out. Furthermore, the proposed algorithm is applied for restoring images with different noise levels.
A PERTURBED QUASI-NEWTON ALGORITHM FOR BOUND-CONSTRAINED GLOBAL OPTIMIZATION Raouf Ziadi, Abdelatif Bencherif-Madani Journal of Computational Mathematics, 2025 This paper presents a stochastic modification of a limited memory BFGS method to solve bound-constrained global minimization problems with a differentiable cost function with no further smoothness. The approach is a stochastic descent method where the deterministic sequence, generated by a limited memory BFGS method, is replaced by a sequence of random variables. To enhance the performance of the proposed algorithm and make sure the perturbations lie within the feasible domain, we have developed a novel perturbation technique based on truncating a multivariate double exponential distribution to deal with bound-constrained problems; the theoretical study and the simulation of the developed truncated distribution are also presented. Theoretical results ensure that the proposed method converges almost surely to the global minimum. The performance of the algorithm is demonstrated through numerical experiments on some typical test functions as well as on some further engineering problems. The numerical comparisons with stochastic and meta-heuristic methods indicate that the suggested algorithm is promising.
An improved conjugate gradient algorithm by adapting a new line search technique Asma Maiza, , Raouf Ziadi, Mohammed A. Saleh, Abdulgader Z. Almaymuni, and Electronic Research Archive, 2025 The conjugate gradient (CG) method is an optimization technique known for its rapid convergence; it has blossomed into significant developments and applications. Numerous variations of CG methods have emerged to enhance computational efficiency and address real-world challenges. This work presents a new conjugate gradient method for solving nonlinear unconstrained optimization problems by introducing a new conjugate gradient parameter. To improve the convergence properties, we have proposed a new inexact line search technique that fits in with the suggested approach and can also be useful for other gradient descent methods. The existence of a steplength that meets the new line search conditions is established. The generated descent direction and the convergence properties of the suggested approach are studied under the new line search conditions, where the global convergence is proven under mild assumptions. The proposed approach is evaluated on various test functions, and a comparison with recent similar algorithms is carried out. Furthermore, the proposed algorithm is applied for restoring images with different noise levels.
An efficient hybrid conjugate gradient method for unconstrained optimization and image restoration problems C. Souli, R. Ziadi, I. Lakhdari, A. Leulmi Iranian Journal of Numerical Analysis and Optimization, 2025 The conjugate gradient (CG) method is an optimization technique known for its rapid convergence; it has blossomed into significant developments and applications. Numerous variations of CG methods have emerged to en-hance computational efficiency and address real-world challenges. In this work, a novel conjugate gradient method is introduced to solve nonlinear unconstrained optimization problems. Based on the combination of PRP (Polak–Ribière–Polyak), HRM (Hamoda–Rivaie–Mamat) and NMFR (new modified Fletcher–Reeves) algorithms, our method produces a descent di-rection without depending on any line search. Moreover, it enjoys global convergence under mild assumptions and is applied successfully on various standard test problems as well as image processing. The numerical results indicate that the proposed method outperforms several existing methods in terms of efficiency.
TWO MODIFIED CONJUGATE GRADIENT METHODS AND THEIR APPLICATION TO IMAGE RESTORATION PROBLEMS Abd Elhamid Mehamdia, Chaib Yacine, Hisham M. Khudhur, Raouf Ziadi Ural Mathematical Journal, 2025 Conjugate gradient methods have significantly contributed to the discovery of minimizes of large-scale unconstrained optimization problems. In this paper, based on the Liu--Storey conjugate gradient method, two modified conjugate gradient methods (named MC1 and MC2 methods) are presented for unconstrained optimization. Under usual assumptions, the two presented methods are proven to be sufficient descent at each iteration. The global convergence results of our methods is established using the strong Wolfe line search (SWLS). Numerical tests demonstrate the effectiveness of the MC1 and MC2 methods when compared to certain existing methods in view of the Dolan and Moré performance profile. Furthermore, the practica applications of these methods in image restoration problems is also considered.
Another Updated Parameter for the Hestenes-Stiefel Conjugate Gradient Method Osman Omer Osman Yousif, Raouf Ziadi, Mohammed A. Saleh, Abdulgader Z. Almaymuni International Journal of Analysis and Applications, 2025 The conjugate gradient (CG) methods are considered as one of the most popular methods for solving linear and non-linear unconstrained optimization problems, especially the problems of large-scale, that is because they are characterized by low memory requirements and strong local and global convergence properties. The method of Hestenes-Stiefel (HS) usually gives good numerical results in the practical computation. However, theoretically, its convergence properties are uncertain. To address the convergence failure of HS method, many choices for its update parameter have been proposed such as the choice of Gilbert and Nocedal in 1992, of Hager and Zhang in 2005, and of Yousif et al. in 2022. In this paper, motivated by these updated parameters, we propose another updated parameter for HS, and hence another CG method which inherits all the convergence properties of Gilbert and Nocedal, Hager and Zhang, and of Yousif et al. and has better numerical results. To show the efficiency and robustness of the new modified method in practice, a numerical experiment was done.
An improved version of Polak-Ribi`ere-Polyak conjugate gradient method with its applications in neural networks training Osman Omer Osman Yousif, , Raouf Ziadi, Abdulgader Z. Almaymuni, Mohammed A. Saleh, , and Electronic Research Archive, 2025 Due to their simplicity, low memory requirements, strong convergence properties, and ability to solve problems of high dimensions, the conjugate gradient (CG) methods are widely used to solve linear and non-linear unconstrained optimization problems. The Polak-Ribière-Polyak (PRP) is considered as one of the most efficient CG methods in practical computation. However, theoretically, its convergence properties are poor. Therefore, many variants of PRP with good numerical results and good convergence properties have been developed, such as Gilbert and Nocedal method (PRP$ ^+ $), Wei-Yau-Liu method (WYL), and Yousif et al. method (OPRP). In this paper, based on PRP$ ^+ $ and OPRP methods, we proposed another modified version of PRP that inherits all the convergence properties of PRP$ ^+ $ and OPRP and has improved numerical results. To show the efficiency and robustness of the new modified method in practice, it was compared with PRP$ ^+ $, WYL, and OPRP when they are all applied under the strong Wolfe line search. At the same time, the new method was applied in deep learning to obtain ideal parameters of some neural network (NN) models during the training process.
An Interior Point Algorithm for Quadratic Programming Based on a New Step-Length Assma Leulmi, Raouf Ziadi, Choubeila Souli, Mohammed A. Saleh, Abdulgader Z. Almaymuni International Journal of Analysis and Applications, 2024 Interior point methods have seen significant advancements in recent decades for solving linear, semi-definite and quadratic programming. Among these methods, the logarithmic barrier methods based on approximate functions have polynomial convergence and are known for their favorable numerical performance. In this work, a new minorant function for the barrier method is proposed for solving convex quadratic problems with inequality constraints. The proposed minorant function allows to compute the steplength easily and quickly, unlike the line search method, which is computationally intensive and time-consuming. Mathematical results concerning the convergence of the algorithm are established. The numerical comparisons with the inexact Wolfe line search technique show that the proposed method is promising and effective.
