New Interior-Point Algorithm for Symmetric Optimization Based on a Positive-Asymptotic Barrier Function

References

• Karmarkar, N. (1984). A new polynomial-time algorithm for linear programming. Combinatorica 4(4):373–395. doi: 10.1007/BF02579150
   Web of Science ®Google Scholar
• Roos, C., Terlaky, T., J.-Ph, V. (2005). Theory and Algorithms for Linear Optimization. New York, NY: Springer.
   Google Scholar
• Wright, S. (1997). Primal-Dual Interior-Point Methods. Philadelphia, PA: SIAM.
   Google Scholar
• Ye, Y. (1997). Interior Point Algorithms, Theory and Analysis. Chichester, UK: John Wiley & Sons.
   Google Scholar
• Klerk, E. D. (2002). Aspects of Semidefinite Programming: Interior Point Algorithms and Selected Applications. Kluwer Academic Publishers.
   Google Scholar
• Alizadeh, F., Goldfarb, D. (2003). Second-order cone programming. Math. Program. 95(1):3–51. doi: 10.1007/s10107-002-0339-5
   Web of Science ®Google Scholar
• Kojima, M., Megiddo, N., Noma, T., Yoshise, A. (1991). A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems. Lecture Notes in Computer Science, Vol. 538. Berlin, Germany: Springer Verlag.
   Google Scholar
• Potra, F. A., Sheng, R. (1997). Predictor-corrector algorithm for solving P*(κ)-matrix LCP from arbitrary positive starting points. Math. Program. 76(1):223–244. doi: 10.1007/BF02614385
   Web of Science ®Google Scholar
• Illés, T., Nagy, M. (2007). A Mizuno-Todd-Ye type predictor-corrector algorithm for sufficient linear complementarity problems. Eur. J. Oper. Res. 181(3):1097–1111. doi: 10.1016/j.ejor.2005.08.031
   Web of Science ®Google Scholar
• Illés, T., Nagy, M., Terlaky, T. (2010). A polynomial path-following interior point algorithm for general linear complementarity problems. J. Glob. Optim. 47(3):329–342. doi: 10.1007/s10898-008-9348-0
   Web of Science ®Google Scholar
• Nesterov, Y., Nemirovskii, A. (1994). Interior Point Polynomial Methods in Convex Programming: Theory and Algorithms, Vol. 13 of SIAM Studies in Applied Mathematics. Philadelphia, PA: SIAM Publications.
   Google Scholar
• Nesterov, Y. E., Todd, M. J. (1997). Self-scaled barriers and interior-point methods for convex programming. Math. Oper. Res. Arch. 22(1):1–42. doi: 10.1287/moor.22.1.1
   Web of Science ®Google Scholar
• Nesterov, Y. E., Todd, M. J. (1998). Primal-dual interior-point methods for self-scaled cones. SIAM J. Optim. 8(2):324–364. doi: 10.1137/S1052623495290209
   Web of Science ®Google Scholar
• Faraut, J., Korányi, A. (1994). Analysis on Symmetric Cones. New York: Oxford University Press.
   Google Scholar
• Faybusovich, L. (2002). A Jordan-algebraic approach to potential-reduction algorithms. Math. Z. 239(1):117–129. doi: 10.1007/s002090100286
   Web of Science ®Google Scholar
• Sturm, J. F. (2000). Similarity and other spectral relations for symmetric cones. Linear Algebra Appl. 312(1–3):135–154. doi: 10.1016/S0024-3795(00)00096-3
   Web of Science ®Google Scholar
• Gu, G., Zangiabadi, M., Roos, C. (2011). Full Nesterov-Todd Step infeasible interior-point method for symmetric optimization. Eur. J. Oper. Res. 214(3):473–484. doi: 10.1016/j.ejor.2011.02.022
   Web of Science ®Google Scholar
• Schmieta, S., Alizadeh, F. (2003). Extension of primal-dual interior point algorithms to symmetric cones. Math. Program. Ser. A. 96(3):409–438. doi: 10.1007/s10107-003-0380-z
   Web of Science ®Google Scholar
• Vieira, M. (2007). Jordan algebraic approach to symmetric optimization. Ph.D. thesis. Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, The Netherlands.
   Google Scholar
• Darvay, Zs. (2002). A new algorithm for solving self-dual linear optimization problems. Studia Univ. Babeş-Bolyai, Ser. Informatica 47(1):15–26.
   Google Scholar
• Darvay, Zs. (2003). New interior point algorithms in linear programming. Adv. Model. Optim. 5(1):51–92.
   Google Scholar
• Achache, M. (2006). A new primal-dual path-following method for convex quadratic programming. Comput. Appl. Math. 25(1):97–110. doi: 10.1590/S0101-82052006000100005
   Google Scholar
• Achache, M. (2010). Complexity analysis and numerical implementation of a short-step primal-dual algorithm for linear complementarity problems. Appl. Math. Comput. 216(7):1889–1895. doi: 10.1016/j.amc.2010.03.015
   Web of Science ®Google Scholar
• Mansouri, H., Pirhaji, M. (2013). A polynomial interior-point algorithm for monotone linear complementarity problems. J. Optim. Theory Appl. 157(2):451–461. doi: 10.1007/s10957-012-0195-2
   Web of Science ®Google Scholar
• Asadi, S., Mansouri, H. (2013). Polynomial interior-point algorithm for P*(κ) horizontal linear complementarity problems. Numer. Algor. 63(2):385–398. doi: 10.1007/s11075-012-9628-0
   Web of Science ®Google Scholar
• Kheirfam, B. (2014). A predictor-corrector interior-point algorithm for P*(κ)-horizontal linear complementarity problem. Numer. Algor. 66(2):349–361. doi: 10.1007/s11075-013-9738-3
   Web of Science ®Google Scholar
• Wang, G. Q., Bai, Y. Q. (2009). A new primal-dual path-following interior-point algorithm for semidefinite optimization. J. Math. Anal. Appl. 353(1):339–349. doi: 10.1016/j.jmaa.2008.12.016
   Web of Science ®Google Scholar
• Wang, G. Q., Bai, Y. Q. (2009). A primal-dual interior-point algorithm for second-order cone optimization with full Nesterov-Todd Step. Appl. Math. Comput. 215(3):1047–1061. doi: 10.1016/j.amc.2009.06.034
   Web of Science ®Google Scholar
• Wang, G. Q., Bai, Y. Q. (2012). A new full Nesterov-Todd Step primal-dual path-following interior-point algorithm for symmetric optimization. J. Optim. Theory Appl. 154(3):966–985. doi: 10.1007/s10957-012-0013-x
   Web of Science ®Google Scholar
• Kheirfam, B. (2013). A new infeasible interior-point method based on Darvay’s technique for symmetric optimization. Ann. Oper. Res. 211(1):209–224. doi: 10.1007/s10479-013-1474-5
   Web of Science ®Google Scholar
• Kheirfam, B. (2014). A predictor-corrector path-following algorithm for symmetric optimization based on Darvay’s technique. Yugosl. J. Oper. Res. 24(1):35–51. doi: 10.2298/YJOR120904016K
   Google Scholar
• Wang, G. Q. (2012). A new polynomial interior-point algorithm for the monotone linear complementarity problem over symmetric cones with full NT-steps. Asia. Pac. J. Oper. Res. 29(02):1250015. doi: 10.1142/S0217595912500157
   Web of Science ®Google Scholar
• Sonnevend, G. (1986). An “analytic center” for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming. In: Prékopa, A., Szelezsán, J., Strazicky, B., eds. System Modelling and Optimization: Proceedings of the 12th IFIP-Conference Held in Budapest, Hungary, September. 1985, Vol. 84 of Lecture Notes in Control and Information Sciences. Berlin, West-Germany: Springer Verlag, pp. 866–876.
   Google Scholar
• Peng, J., Roos, C., Terlaky, T. (2002). Self-Regular Functions: A New Paradigm for Primal-Dual Interior-Point Methods. Princeton University Press.
   Google Scholar
• Darvay, Zs., Papp, I.-M., Takács, P.-R. (2016). Complexity analysis of a full-Newton Step interior-point method for linear optimization. Period. Math. Hung. 73(1):27–42. doi: 10.1007/s10998-016-0119-2
   Web of Science ®Google Scholar