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An infeasible full-NT step interior point algorithm for CQSCO

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Abstract

In this paper, we propose a full Nesterov-Todd (NT) step infeasible interior-point algorithm for convex quadratic symmetric cone optimization based on Euclidean Jordan algebra. The algorithm uses only one feasibility step in each main iteration. The complexity result coincides with the best-known iteration bound for infeasible interior-point methods.

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References

  1. Bai, Y.Q., Zhang, L.P.: A full-Newton step interior-point algorithm for symmetric cone convex quadratic optimization. J. Ind. Manag. Optim. 7(4), 891–906 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  2. Faraut, J., Kornyi, A.: Analysis on Symmetric Cones, Oxford Mathematical Monographs. The Clarendon Press Oxford University Press, New York (1994)

    Google Scholar 

  3. Faybusovich, L.: A Jordan-algebraic approach to potential-reduction algorithms. Mathematicsche Zeitschrift 239(1), 117–129 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Faybusovich, L.: Linear systems in Jordan algebras and primal-dual interior-point algorithms. J. Comput. Appl. Math. 86, 149–175 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  5. Kheirfam, B., Mahdavi-Amiri, N.: A full Nesterov-Todd step infeasible interior-point algorithm for symmetric cone linear complementarity problem. Bull. Iranian Math. Soc. 40(3), 541–564 (2014)

    MathSciNet  MATH  Google Scholar 

  6. Kheirfam, B.: A new complexity analysis for full-Newton step infeasible interior-point algorithm for horizontal linear complementarity problems. J. Optim. Theory Appl. 161(3), 853–869 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  7. Kheirfam, B.: A new infeasible interior-point method based on Darvay’s technique for symmetric optimization. Ann. Oper. Res. 211(1), 209–224 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kheirfam, B.: A full Nesterov-Todd step infeasible interior-point algorithm for symmetric optimization based on a specific kernel function, Numer. Algebra Control Optim. 3(4), 601–614 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kheirfam, B.: A full step infeasible interior-point method for Cartesian P ∗(κ)-SCLCP. Optim. Lett. 10(3), 591–603 (2016)

  10. Kheirfam, B.: An improved full-Newton step O(n) infeasible interior-point method for horizontal linear complementarity problem. Numer. Algorithms. 71(3), 491–503 (2016)

  11. Kheirfam, B.: A corrector-predictor path-following method for convex quadratic symmetric cone optimization. J. Optim. Theory Appl. 164(1), 246–260 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kojima, M., Megiddo, N., Mizuno, S.: A primal-dual infeasible-interior-point algorithm for linear programming. Math. Program. 61, 263–280 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  13. Li, L., Toh, K.C.: A polynomial-time inexact interior-point method for convex quadratic symmetric cone programming. J. Math. Indus. 2, 199–212 (2010B)

    MathSciNet  MATH  Google Scholar 

  14. Lustig, I.J.: Feasibility issues in a primal-dual interior-point methods for linear programming. Math. Progrem. 49, 145–162 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  15. Maros, I., Meszaros, C.: Departmental Technical Report DOC 97/6, Department of Computing, Imperial College, London, U.K., A repository of convex quadratic programming problems

  16. Nesterov, Y.E., Todd, M.J.: Self-scaled barriers and interior-point methods for convex programming. Math. Oper. Res. 22, 1–42 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  17. Rangarajan, B.K.: Polynomial convergence of infeasible interior-point methods over symmetric cones. SIAM J. Optim. 16(4), 1211–1229 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  18. Roos, C.: A full-Newton step O(n) infeasible interior-point algorithm for linear optimization. SIAM J. Optim. 16, 1110–1138 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  19. Roos, C.: An improved and simplified full-Newton step O(n) infeasible interior-point method for linear optimization. SIAM J. Optim. 25(1), 102–114 (2015)

    Article  MathSciNet  Google Scholar 

  20. Roos, C., Terlaky, T., Vial, J-Ph: Theory and Algorithms for Linear Optimization. An Interior-Point Approach. Wiley, Chichester (1997)

    MATH  Google Scholar 

  21. Schmieta, S.H., Alizadeh, F.: Extension of primal-dual interior-point algorithm to symmetric cones. Math. Program. 96(3), 409–438 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  22. Sturm, J.F.: Similarity and other spectral relations for symmetric cones. Linear Algebra Appl. 312(1-3), 135–154 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  23. Wang, G.Q., Zhang, Z.H., Zhu, D.T.: On extending primal-dual interior-point method for linear optimization to convex quadratic symmetric cone optimization. Numer. Funct. Anal. Optim. 34(5), 576–603 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  24. Wang, G.Q., Yu, C.J., Teo, K.L.: A new full Nesterov-Todd step feasible interior-point method for convex quadratic symmetric cone optimization. Appl. Math. Comput. 221, 329–343 (2013)

    MathSciNet  MATH  Google Scholar 

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Correspondence to Behrouz Kheirfam.

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Kheirfam, B. An infeasible full-NT step interior point algorithm for CQSCO. Numer Algor 74, 93–109 (2017). https://doi.org/10.1007/s11075-016-0140-9

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  • DOI: https://doi.org/10.1007/s11075-016-0140-9

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