Open Access
Research Article
Interior-point method for CQP problems employing a novel trigonometric kernel function
*I. TouilCorresponding authortouilimene@univ-jijel.dzDepartment of Mathematics Laboratory of Pure and Applied Mathematics Mohammed Seddik Ben Yahia UniversityJijel, AlgeriaView full profile → , W. Chikouchew_chikouche@yahoo.comDepartment of Mathematics Laboratory of Pure and Applied Mathematics Mohammed Seddik Ben Yahia UniversityJijel, AlgeriaView full profile → , Dj. Benterkidjbenterki@univ-setif.dzDepartment of Mathematics Laboratory of Fundamental and Numerical Mathematics Ferhat Abbas UniversitySetif, 19000, AlgeriaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 07 Feb 2023
- Published Online:
- 02 Feb 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIOS-1464
- Pages:
- 437–453
Abstract
We introduce a primal-dual interior-point approach to address convex quadratic programming dilemmas, utilizing a novel class of efficient parametric kernel functions. Using basic analytical tools, we establish that the developed algorithm has an iteration bound of O((p+1)np+2/2(p+1)log n/e) for the large-update method, where p is a parameter with p ≥ 2. For the small-update method, we obtain the best known iteration bound, namely O(p2√n log n/e) [5, 7]. Finally, we provide numerical experiments that illustrate the algorithm’s effectiveness.
Keywords
Subject Classifications
90C2090C2590C51
References
[1] E. I. Abd El-Latif and M. I. Moussa, “Information hiding using artificial DNA sequences based on Gaussian kernel function,” Journal of Information and Optimization Sciences, vol. 40, no. 6, pp. 1181-1194 (2019). doi: 10.1080/02522667.2017.1413041.[2] M. Achache, “A new primal-dual path-following method for convex quadratic programming,” Computational & Applied Mathematics, vol. 25, no. 1, pp. 97-110 (2006).[3] F. Alizadeh and D. Goldfarb, “Second-order cone programming,” Mathematical Programming, Series B, vol. 95, pp. 3–51 (2003).[4] Y. Q. Bai, M. E. L. Ghami, and C. Roos, “A comparative study of kernel functions for primal-dual interior-point algorithms in linear optimization,” SIAM Journal on Optimization, vol. 15, pp. 101-128 (2004).[5] M. Bouafia, D. Benterki, and A. Yassine, “An efficient primal-dual interior-point method for linear programming problems based on a new kernel function with a trigonometric barrier term,” Journal of Optimization Theory and Applications, vol. 170, pp. 528-545 (2016).[6] N. Boudjellal, H. Roumili, and D. Benterki, “A primal-dual interior-point algorithm for convex quadratic programming based on a new parametric kernel function,” Optimization (2020). doi: 10.1080/02331934.2020.1751156.[7] S. Guerdouh, W. Chikouche, and I. Touil, “An efficient primal-dual interior-point algorithm for linear optimization problems based on a novel parameterized kernel function with a hyperbolic barrier term,” (2021). halshs-03228790.[8] F. S. Hafshejani and A. F. Jahromi, “An interior point method for P*(k)–horizontal linear complementarity problem based on a new proximity function,” Journal of Applied Mathematics and Computation (2019). doi: 10.1007/s12190-019-01284-9.[9] F. S. Hafshejani and Z. Moaberfard, “An interior-point algorithm for linearly constrained convex optimization based on kernel function and application in non-negative matrix factorization,” Optimization Engineering, vol. 21, pp. 1019–1051 (2020). doi: 10.1007/s11081-020-09514-x.[10] F. S. Hafshejani and Z. Moaberfard, “A new trigonometric kernel function for support vector machine,” Iran Journal of Computer Science, vol. 6, no. 2, pp. 1-9 (2022). doi: 10.1007/s42044-022-00130-9.[11] E. H. Houssein, A. Hamad, A. E. Hassanien, and A. A. Fahmy, “Epileptic detection based on whale optimization enhanced support vector machine,” Journal of Information and Optimization Sciences, vol. 40, no. 3, pp. 699-723 (2019). doi: 10.1080/02522667.2018.1453671.[12] M. A. Noor, “On the nonlinear complementarity problem,” Journal of Mathematical Analysis and Applications, vol. 123, no. 2, pp. 455-460 (1987).[13] C. Roos, T. Terlaky, and J. P. Vial, Theory and Algorithms for Linear Optimization: An Interior Point Approach, John Wiley & Sons, Chichester, UK (1997).[14] I. Touil and D. Benterki, “A primal-dual interior-point method for the semidefinite programming problem based on a new kernel function,” Journal of Nonlinear Functional Analysis, vol. 2019, Article ID 25 (2019).[15] I. Touil and W. Chikouche, “Primal-dual interior point methods for semidefinite programming based on a new type of kernel functions,” Filomat, vol. 34, no. 12, pp. 3957-3969 (2020).[16] I. Touil and W. Chikouche, “Polynomial-time algorithm for linear programming based on a kernel function with hyperbolic-logarithmic barrier term,” PJM, vol. 11, pp. 127-135 (2022).
Views: 85Downloads: 6Citations: 0
