An Efficient Primal–Dual Interior Point Method for Linear Programming Problems Based on a New Kernel Function with a Trigonometric Barrier Term
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In this paper, we present a primal–dual interior point method for linear optimization problems based on a new efficient kernel function with a trigonometric barrier term. We derive the complexity bounds for large and small-update methods, respectively. We obtain the best known complexity bound for large update, which improves significantly the so far obtained complexity results based on a trigonometric kernel function given by Peyghami et al. The results obtained in this paper are the first to reach this goal.
KeywordsLinear optimization Kernel function Interior point methods Complexity bound
Mathematics Subject Classification90C05 90C31 90C51
The authors are very grateful and would like to thank the anonymous referees for their suggestions and helpful comments, which significantly improved the presentation of this paper.
- 8.Cai, X.Z., Wang, G.Q., El Ghami, M., Yue, Y.J.: Complexity analysis of primal-dual interior-point methods for linear optimization based on a new parametric kernel function with a trigonometric barrier term. Abstr. Appl. Anal., Art. ID 710158, 11 (2014)Google Scholar
- 9.Karmarkar, N.K.: A new polynomial-time algorithm for linear programming. In: Proceedings of the 16th Annual ACM Symposium on Theory of Computing, vol. 4, pp. 373–395 (1984)Google Scholar
- 10.Bai, Y.Q., Roos, C.: A primal-dual interior point method based on a new kernel function with linear growth rate. In: Proceedings of the 9th Australian Optimization Day, Perth, Australia (2002)Google Scholar
- 14.Sonnevend, G.: An “analytic center” for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming. In: Prekopa, A., Szelezsan, J., Strazicky, B. (eds.) System Modelling and Optimization: Proceedings of the 12th IFIP-Conference, Budapest, Hungary, 1985. Lecture Notes in Control and Information Science, vol. 84, pp. 866–876. Springer, Berlin (1986)Google Scholar