Abstract
In this paper, we propose a primal-dual interior point method for linear optimization (LO) based on a new parameterized kernel function. The proposed kernel function is a generalization of the one used recently in Bai et al. (SIAM J Optim 15:101–128, 2004) for LO. The investigation according to it yields the best known iteration bound \(O\left( \sqrt{n} \log n \log \frac{n}{\epsilon }\right) \) for large-update algorithm and thus improves the iteration bound obtained in Bai et al. (SIAM J Optim 15:101–128, 2004) for large-update algorithm. Finally, we present few numerical results to demonstrate the efficiency of the proposed algorithm.
Similar content being viewed by others
References
Amini, K., Haseli, A.: A new proximity function generating the best known iteration bounds for both large-update and small-updatebinterior point methods. ANZIAM 49, 259–270 (2007)
Bai, Y.Q., El Ghami, M., Roos, C.: A comparative study of kernel functions for primal-dual interior point algorithms in linear optimization. SIAM J. Optim. 15(1), 101–128 (2004)
Bai, Y.Q., Wang, G.Q., Roos, C.: A new kernel function yielding the best known iteration bounds for primal-dual interior point method. Acta Math. Sinica 25(12), 2169–2178 (2009)
El Ghami, M., Ivanov, I., Melissen, J.B.M., Roos, C., Steihaug, T.: A polynomial-time algorithm for linear optimization based on a new class of kernel functions. J. Comput. Appl. Math. 224, 500–513 (2009)
Peng, J., Roos, C., Terlaky, T.: Self-regular functions and new search directions for linear and semidefinite optimization. Math. Program. 93, 129–171 (2002)
Peng, J., Roos, C., Terlaky, T.: Self-Regularity. A new paradigm for Primal-Dual Interior Point Algorithm. Princeton University Press, Princeton (2002)
Roos, C., Terlaky, T., Vial, J.Ph.: Theory and Algorithms for Linear Pptimization. An Interior Point Approach. Wiley, Chichester (1997)
Wang, G.Q., Bai, Y.Q., Liu, Y., Zhang, M.: A new primal-dual interior-point algorithm for convex quadratic optimization. J. Shangai Univ. (Engl. Ed.) 12(3), 180–196 (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Achache, M. A new parameterized kernel function for LO yielding the best known iteration bound for a large-update interior point algorithm. Afr. Mat. 27, 591–601 (2016). https://doi.org/10.1007/s13370-015-0363-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13370-015-0363-2