Complexity analysis of primal-dual interior-point methods for linear optimization based on a new efficient Bi-parameterized kernel function with a trigonometric barrier term

Abstract

In this paper we are generalizing the efficient kernel function with trigonometric barrier term given by (M. Bouafia, D. Benterki and A. Yassine, J. Optim. Theory Appl. 170 (2016) 528–545). Using an elegant and simple analysis and under some easy to check conditions, we explore the best complexity result for the large update primal-dual interior point methods for linear optimization. This complexity estimate improves results obtained in (X. Li and M. Zhang, Oper. Res. Lett. 43 (2015) 471–475; M.R. Peyghami and S.F. Hafshejani, Numer. Algo. 67 (2014) 33–48; M. Bouafia, D. Benterki and A. Yassine, J. Optim. Theory Appl. 170 (2016) 528–545). Our comparative numerical experiments on some test problems consolidate and confirm our theoretical results according to which the new kernel function has promising applications compared to the kernel function given by (M. Bouafia and A. Yassine, Optim. Eng. 21 (2020) 651–672). Moreover, the comparative numerical study that we have established favors our new kernel function better than other best trigonometric kernel functions (M. Bouafia, D. Benterki and A. Yassine, J. Optim. Theory Appl. 170 (2016) 528–545; M. Bouafia and A. Yassine, Optim. Eng. 21 (2020) 651–672).