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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 65, 2016 - Issue 2
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Articles

A full Nesterov–Todd step infeasible-interior-point algorithm for Cartesian P*(κ) horizontal linear complementarity problems over symmetric cones

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Pages 539-565 | Received 27 Apr 2014, Accepted 28 May 2015, Published online: 08 Jul 2015

References

  • Faybusovich L. Euclidean Jordan algebras and interior-point algorithm. Positivity. 1997;14:331–357.
  • Faybusovich L. Linear systems in Jordan algebras and primal-dual interior-point algorithms.J. Comput. Appl. Math. 1997;86:149–175.
  • Faybusovich L. A Jordan-algebraic approach to potential-reduction algorithms. Math. Z. 2002;239:117–129.
  • Schmieta SH, Alizadeh F. Extension of primal-dual interior point algorithms to symmetric cones. Math. Program. 2003;96:409–438.
  • Gu G, Zangiabadi M, Roos C. Full Nesterov--Todd step interior-point methods for symmetric optimization. Eur. J. Oper. Res. 2011;214:473–484.
  • Anitescu M, Lesaja G, Potra FA. Equivalence between different formulations of the linear complementarity problem. Optim. Methods Softw. 1997;7:265–290.
  • Kojima M, Megiddo N, Noma T, Yoshise A. A unified approach to interior point algorithms for linear complementarity problems. Lecture notes in computer science. Springer-Verlag:New York (NY); 1991.
  • Valiaho H. P*-matrices are just sufficient. Linear Algebra Appl. 1996;239:103–108.
  • Cottle RW, Pang JS, Venkateswaran V. Sufficient matrices and the linear complementarity problem. Linear Algebra Appl. 1989;114:231–249.
  • Gurtuna F, Petra C, Potra FA, Shevchenko O, Vancea A. Corrector-Predictor methods for sufficient linear complementarity problems. Comput. Optim. Appl. 2011;48:453–485.
  • Wang GQ, Bai YQ. Polynomial interior-point algorithms for P*(κ) horizontal linear complementarity problem. J. Comput. Appl. Math. 2009;233:248–263.
  • Asadi S, Mansouri H. Polynomial interior-point algorithm for P*(κ) horizontal linear complementarity problems. Numer. Algorithms. 2012;63:385–398.
  • Asadi S, Mansouri H. A new full-Newton step O(n) infeasible interior-point algorithm for P*(κ)-horizontal linear complementarity problems. Comp. Sci. J. Moldova. 2014;22:37–61.
  • Gowda MS, Sznajder R. Some global uniqueness and solvability results for linear complementarity problems over symmetric cones. SIAM J. Optim. 2007;18:461–481.
  • Yoshise A. Interior point trajectories and a homogeneous model for nonlinear complementarity problems over symmetric cones. SIAM J. Optim. 2007;17:1129–1153.
  • Luo ZY, Xiu NH. Path-following interior point algorithms for the Cartesian P*(κ)-LCP over symmetric cones. Sci. China Ser. A: Math. 2009;52:1769–1784.
  • Chen X, Qi HD. Cartesian P-property and its applications to the semidefinite linear complementarity problem. Math. Program. 2006;106:177–201.
  • Kong LC, Tancel L, Xiu NH. Vector-valued implicit lagrangian for symmetric cone complementarity problems, Research Report CORR 2006-24. Depaetment of combinatorics and optimization. Waterloo: University of Waterloo; 2006.
  • Wang GQ, Lesaja G. Full Nestero-Todd step feasible interior-point method for the Cartesian P*(κ)-SCLCP. Optim. Methods Softw. 2013;28:600–618.
  • Roos C. A full-Newton step O(n) infeasible interior-point algorithm for linear optimization. SIAM J. Optim. 2006;16:1110–1136.
  • Zangiabadi M, Gu G, Roos C. A full Nesterov-Todd step infeasible interior-point method for second-order cone optimization. J. Optim. Theory. Appl. 2013;158:816–858.
  • Gu G. Full-step interior-point methods for symmetric optimization [PhD thesis]. Delft University of Technology. 2009.
  • Faraut J, Koranyi A. Analysis on symmetric cones. Oxford mathematical monographs. The Clarendon Press, Oxford University Press, Oxford Science Publications: New York (NY); 1994.
  • Vieira VC. 2007. Jordan algebraic approach to symmetric optimization [PhD thesis]. Delft University of Technology.
  • Rangarajan BK. Polynomial convergence of infeasible-interior-point methods over symmetric cones. SIAM J. Optim. 2006;16:1211–1229.
  • Sturm JF. Similarity and other spectral relations for symmetric cones. Linear Algebra Appl. 2000;312:135–154.
  • Asadi S, Mansouri H, Zangiabadi M. On the P*(κ) horizontal linear complementarity problems over Cartesian product of symmetric cones. Optim. Methods Softw. forthcoming. Available from: http://dx.doi.org/10.1080/10556788.2015.1058795.
  • Potra FA, Stoer J. On a class of superlinearly convergent polynomial time interior point methods for sufficient LCP. SIAM J. Optim. 2009;20:1333–1363.
  • Roos C, Terlaky T, Vial J-Ph. Interior point methods for linear optimization. New York (NY): Springer; 2006.

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