Abstract
Recently, Roos (SIAM J Optim 16(4):1110–1136, 2006) presented a primal-dual infeasible interior-point algorithm that uses full-Newton steps and whose iteration bound coincides with the best known bound for infeasible interior-point algorithms. In the current paper we use a different feasibility step such that the definition of the feasibility step in Mansouri and Roos (Optim Methods Softw 22(3):519–530, 2007) is a special case of our definition, and show that the same result on the order of iteration complexity can be obtained.
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Achache, M.: A new primal-dual path-following method for convex quadratic programming. Comput. Appl. Math. 25(1), 97–110 (2006)
Mansouri, H., Roos, C.: Simplified O(nL) infeasible interior-point algorithm for linear optimization using full-Newton step. Optim. Methods Softw. 22(3), 519–530 (2007)
Mizuno, S.: Polynomiality of infeasible-interior-point algorithms for linear programming. Math. Program. 67(1), 109-119 (1994)
Peng, J., Roos, C., Terlaky, T.: New complexity analysis of the primal-dual Newton method for linear optimization. Ann. Oper. Res. 99(1), 23–39 (2000)
Peng, J., Roos, C., Terlaky, T.: A new class of polynomial primal-dual methods for linear and semidefinite optimization. Eur. J. Oper. Res. 143(2), 234–256 (2002)
Peng, J., Roos, C., Terlaky, T.: Self-Regularity: A New Paradigm for Primal-Dual Interior-Point Algorithms. Princeton University Press, Princeton (2002)
Potra, F.A.: An infeasible interior-point predictor-corrector algorithm for linear programming. SIAM J. Optim. 6(1), 19–32 (1996)
Roos, C.: A full-Newton step O(n) infeasible interior-point algorithm for linear optimization. SIAM J. Optim. 16(4), 1110–1136 (2006)
Roos, C., Terlaky, T., Vial, J.-Ph.: Theory and Algorithms for Linear Optimization. An Interior Approach. Wiley, Chichester (1997)
Salahi, M., Terlaky, T., Zhang, G.: The complexity of self-regular proximity based infeasible IPMs. Comput. Optim. Appl. 33(2), 157–185 (2006)
Sun, W., Yuan, Y.: Optimization Theory and Methods: Nonlinear Programming. Springer, New York (2006)
Todd, M.J., Ye, Y.: A lower bound on the number of iterations of long-step and polynomial interior-point linear programming algorithms. Ann. Oper. Res. 62(1), 233–252 (1996)
Ye, Y.: Interior Point Algorithms: Theory and Analysis. Wiley, New York (1997)
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Liu, Z., Sun, W. An infeasible interior-point algorithm with full-Newton step for linear optimization. Numer Algor 46, 173–188 (2007). https://doi.org/10.1007/s11075-007-9135-x
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DOI: https://doi.org/10.1007/s11075-007-9135-x