Nakhaei Amroudi, A., Shojaeifard, A., Pirhaji, M. (2019). A Full-NT Step Infeasible Interior-Point Algorithm for Mixed Symmetric Cone LCPs. Sahand Communications in Mathematical Analysis, 14(1), 127-146. doi: 10.22130/scma.2018.67206.260

Ali Nakhaei Amroudi; Ali Reza Shojaeifard; Mojtaba Pirhaji. "A Full-NT Step Infeasible Interior-Point Algorithm for Mixed Symmetric Cone LCPs". Sahand Communications in Mathematical Analysis, 14, 1, 2019, 127-146. doi: 10.22130/scma.2018.67206.260

Nakhaei Amroudi, A., Shojaeifard, A., Pirhaji, M. (2019). 'A Full-NT Step Infeasible Interior-Point Algorithm for Mixed Symmetric Cone LCPs', Sahand Communications in Mathematical Analysis, 14(1), pp. 127-146. doi: 10.22130/scma.2018.67206.260

Nakhaei Amroudi, A., Shojaeifard, A., Pirhaji, M. A Full-NT Step Infeasible Interior-Point Algorithm for Mixed Symmetric Cone LCPs. Sahand Communications in Mathematical Analysis, 2019; 14(1): 127-146. doi: 10.22130/scma.2018.67206.260

A Full-NT Step Infeasible Interior-Point Algorithm for Mixed Symmetric Cone LCPs

^{}Department of Mathematics and Statistics, Imam Hossein Comprehensive University, Tehran, Iran.

Abstract

An infeasible interior-point algorithm for mixed symmetric cone linear complementarity problems is proposed. Using the machinery of Euclidean Jordan algebras and Nesterov-Todd search direction, the convergence analysis of the algorithm is shown and proved. Moreover, we obtain a polynomial time complexity bound which matches the currently best known iteration bound for infeasible interior-point methods.

[1] M. Achache, Complexity analysis and numerical implementation of a short-step primal-dual algorithm for linear complementarity problems, Appl. Math. Comput., 216 (2010), pp. 1889-1895.

[2] M. Achache and R. Khebchache, A full-Newton step feasible weighted primal-dual interior-point algorithm for monotone LCP, Afr. Mat., 26 (2015), pp. 139-151.

[3] J. Faraut and A. Koranyi, Analysis on symmetric cones, Oxford University Press, New York, 1994.

[4] L. Faybusovich, Euclidean Jordan algebras and interior-point algorithms, Positivity, 1 (1997), pp. 331-357.

[5] R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge 1986.

[6] M. Kojima, N. Megiddo, T. Noma, and A. Yoshise, A unified approach to interior point algorithms for linear complementarity problems, in: Lecture Notes in Computer Science, vol. 538, Springer-Verlag, Berlin, Germany 1991.

[7] Y. Lin and A. Yoshise, A homogeneous model for mixed complementarity problems over symmetric cones, Vietnam J. Math., 35 (2007), pp. 541-561.

[8] H. Masouri and M. Pirhaji, A polynomial interior-point algorithm for monotone linear complementarity problems, J. Optim. Theory Appl., 157 (2013), pp. 451-461.

[9] H. Masouri, M. Zangiabadi, and M. Pirhaji, A full Newton step $O(n)$ infeasible-interior-point algorithm for linear complementarity problems, Nonlinear Anal., Real World Appl., 12 (2011), pp. 454-561.

[10] H. Masouri, M. Zangiabadi, and M. Pirhaji, A path-following feasible interior-point algorithm for mixed symmetric cone linear complementarity problems, Journal of New Researches in Mathematics, 1 (2016), pp. 109-120.

[11] S.H. Schmieta and F. Alizadeh, Extension of primal dual interior-point algorithms to symmetric cones, Math. Program. Ser. A, 96 (2003), pp. 409-438.

[12] J.F. Sturm, Similarity and other spectral relations for symmetric cones, Linear Algebra Appl. 312 (2000), pp. 135-154.

[13] G.Q. Wang, Y. Yue, and X.Z. Ci, Weighthed-path-following interior-point algorithm to monotone mixed linear complementarity problem, Fuzzy Inf. Eng., 4 (2009), pp. 435-445.

[14] M. Zangiabadi, G. Gu, and C. Roos, A full Nesterov Todd step infeasible interior-point method for second-order cone optimization, J. Optim. Theory. Appl., 158 (2013), pp. 816-858.