Solution of Monotone Complementarity and General Convex Programming Problems Using a Modified Potential Reduction Interior Point Method

Published Online:https://doi.org/10.1287/ijoc.2016.0715

References

  • Andersen ED (2000) On primal and dual infeasibility certificates in a homogeneous model for convex optimization. SIAM J. Optim. 11(2):380–388.CrossrefGoogle Scholar
  • Andersen ED, Ye Y (1998) A computational study of the homogeneous algorithm for large-scale convex optimization. Comput. Optim. Appl. 10(3):243–269.CrossrefGoogle Scholar
  • Andersen ED, Ye Y (1999) On a homogeneous algorithm for the monotone complementarity problem. Math. Programming 84(2): 375–399.CrossrefGoogle Scholar
  • Andersen ED, Roos C, Terlaky T (2003) On implementing a primal-dual interior-point method for conic quadratic optimization. Math. Programming 95(2):249–277.CrossrefGoogle Scholar
  • Bazarra MS, Sherali HD, Shetty CM (1993) Nonlinear Programming: Theory and Algorithms, 2nd ed. (John Wiley & Sons, New York).Google Scholar
  • Bunch JR, Parlett BN (1971) Direct methods for solving symmetric indefinite systems of linear equations. SIAM J. Numerical Anal. 8(4):639–655.CrossrefGoogle Scholar
  • Cafieri S, D’Apuzzo M, De Simone V, di Serafino D, Toraldo G (2007) Convergence analysis of an inexact potential reduction method for convex quadratic programming. J. Optim. Theory Appl. 135(3):355–366.CrossrefGoogle Scholar
  • D’Apuzzo M, De Simone V, di Serafino D (2010) On mutual impact of numerical linear algebra and large-scale optimization with focus on interior point methods. Comput. Optim. Appl. 45(2):283–310.CrossrefGoogle Scholar
  • Dolan E, Moré J (2002) Benchmarking optimization software with performance profiles. Math. Programming 91(2):201–213.CrossrefGoogle Scholar
  • Duff IS (2004) MA57—A code for the solution of sparse symmetric definite and indefinite systems. ACM Trans. Math. Software 30(2):118–144.CrossrefGoogle Scholar
  • Fourer R, Mehrotra S (1993) Solving symmetrical indefinite systems in an interior-point method for linear-programming. Math. Programming 62(1):15–39.CrossrefGoogle Scholar
  • Goldfarb D, Mehrotra S (1988) A relaxed variant of Karmarkar’s algorithm. Math. Programming 40(3):285–315.Google Scholar
  • Gondzio J (1996) Multiple centrality corrections in a primal-dual method for linear programming. Comput. Optim. Appl. 6(2): 137–156.CrossrefGoogle Scholar
  • Kojima M, Mizuno S, Yoshise A (1991) An O(nL) iteration potential reduction algorithm for linear complementary problems. Math. Programming 50(1):331–342.CrossrefGoogle Scholar
  • Luo Z-Q, Sturm JF, Zhang S (2000) Conic convex programming and seld-dual embedding. Optim. Method Software 14(3):169–218.CrossrefGoogle Scholar
  • Maros I, Mézáros C (1999) A repository of convex quadratic programming problems. Optim. Methods Software 11(1–4):671–681.CrossrefGoogle Scholar
  • Mehrotra S (1992) On the implementation of a primal-dual interior point method. SIAM J. Optim. 2(4):575–601.CrossrefGoogle Scholar
  • Mehrotra S, Huang K-L (2012) Computational experience with a modified potential reduction algorithm for linear programming. Optim. Methods Software 27(4–5):865–891.CrossrefGoogle Scholar
  • Nesterov YE, Todd MJ (1997) Self-scaled barriers and interior-point methods for convex programming. Math. Oper. Res. 22(1):1–42.LinkGoogle Scholar
  • Potra FA, Ye Y (1996) Interior-point methods for nonlinear complementarity problems. J. Optim. Theory Appl. 88(3):617–647.CrossrefGoogle Scholar
  • Rockafellar RT (1996) Convex Analysis (Princeton University Press, Princeton, NJ).Google Scholar
  • Skajaa A, Ye Y (2015) A homogeneous interior-point algorithm for nonsymmetric convex conic optimization. Math. Programming 150(2):391–422.CrossrefGoogle Scholar
  • Sturm JF (1999) Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Method Software 11(1–4): 625–653.CrossrefGoogle Scholar
  • Tanabe K (1988) Centered newton method for mathematical programming. Iri M, Yajima K, eds. System Model. Optim. Proc. 13th IFIP Conf., Tokyo, 197–206.Google Scholar
  • Todd MJ, Ye Y (1990) A centered projective algorithm for linear programming. Math. Oper. Res. 15(3):508–529.LinkGoogle Scholar
  • Vanderbei RJ (1995) Symmetric quasi-definite matrices. SIAM J. Optim. 5(1):100–113.CrossrefGoogle Scholar
  • Xu X, Hung P, Ye Y (1996) A simplified homogeneous and self-dual linear programming algorithm and its implementation. Ann. Oper. Res. 62(1):151–171.CrossrefGoogle Scholar
  • Ye Y, Todd MJ, Mizuno S (1994) An O(nL)-iteration homogeneous and self-dual linear programming algorithm. Math. Oper. Res. 19(1):53–67.LinkGoogle Scholar
  • Yoshise A (2006) Interior point trajectories and a homogeneous model for nonlinear complementarity problems over symmetric cones. SIAM J. Optim. 17(4):1129–1153.CrossrefGoogle Scholar
  • Zhang S (2004) A new self-dual embedding method for convex programming. J. Global Optim. 29(4):479–496.CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.