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Original Articles

Infeasible constraint-reduced interior-point methods for linear optimization

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Pages 801-825 | Received 20 Nov 2010, Accepted 09 May 2011, Published online: 14 Sep 2011

References

  • Armand , P. 2003 . A quasi-Newton penalty barrier method for convex minimization problems . Math. Program. , 26 : 5 – 34 .
  • Benson , H. Y. and Shanno , D. F. 2007 . An exact primal–dual penalty method approach to warmstarting interior-point methods for linear programming . Comput. Optim. Appl. , 38 : 371 – 399 .
  • Benson , H. Y. , Sen , A. and Shanno , D. F. Interior-point methods for nonconvex nonlinear programming: Convergence analysis and computational performance, . http://rutcor.rutgers.edu/~shanno/converge5.pdf (2009).
  • Benson , H. Y. , Sen , A. , Shanno , D. F. and Vanderbei , R. J. 2006 . Interior-point algorithms, penalty methods and equilibrium problems . Comput. Optim. Appl. , 34 : 155 – 182 .
  • Dantzig , G. and Ye , Y. A build-up interior-point method for linear programming: Affine scaling form . Working paper, Department of Management Science, University of Iowa, 1991
  • Fiacco , A. V. and McCormick , G. P. Nonlinear Programming: Sequential Unconstrained Minimization Techniques . Society for Industrial and Applied Mathmatics, Philadelphia, PA, 1990
  • Fletcher , J. W. 1995 . Identification of UH-60 stability derivative models in hover from flight test data . J. Amer. Helicopter Soc. , 40 : 32 – 46 .
  • Goodwin , G. C. , Seron , M. M. and Dona , J. A.D. 2005 . Constrained Control and Estimation: an Optimisation Approach , London : Springer .
  • den Hertog , D. , Roos , C. and Terlaky , T. Adding and deleting constraints in logarithmic barrier method for linear programming problems . Shell report, AMER 92-001, 1992
  • He , M. Y. , Kiemb , M. , Tits , A. L. , Greenfield , A. and Sahasrabudhe , V. 2010 . Constraint-reduced interior-point optimization for model predictive rotorcraft control . American Control Conference . 2010 . pp. 2088 – 2094 . Baltimore , MD : American Automatic Control Council .
  • Jung , J. H. , O'Leary , D. P. and Tits , A. L. Adaptive constraint reduction for convex quadratic programming . Comput. Optim. Appl. , (published on-line as of March 2010), DOI: 10.1007/s10589–010–9324–8
  • Leyffer , S. , Calva , G. L. and Nocedal , J. 2006 . Interior methods for mathematical programs with complementarity constraints . SIAM J. Optim. , 17 : 52 – 77 .
  • Mehrotra , S. 1992 . On the implementation of a primal–dual interior point method . SIAM J. Optim. , 2 : 575 – 601 .
  • Nicholls , S. O. Column generation in infeasible predictor–corrector methods for solving linear programs . Ph.D. Thesis, University of Maryland, 2009
  • Potra , F. A. 1994 . A quadratically convergent predictor–corrector method for solving linear programs from infeasible starting points . Math. Program. Ser. A and B , 67 : 383 – 406 .
  • Potra , F. A. 1996 . An infeasible-interior-point predictor–corrector algorithm for linear programming . SIAM J. Optim. , 6 : 19 – 32 .
  • Saigal , R. On the primal–dual affine scaling method . Technical report, Department of Industrial and Operational Engineering, The University of Michigan, 1994
  • Saigal , R. 1996 . A simple proof of a primal affine scaling method . Ann. Oper. Res. , 62 : 303 – 324 .
  • Sen , A. and Shanno , D. F. Convergence analysis of an interior-point method for mathematical programs with equilibrium constraints . http://rutcor.rutgers.edu/~shanno/IPMPEC2.pdf(2006)
  • Stewart , G. W. 1989 . On scaled projections and pseudo-inverses . Linear Algebra Appl. , 112 : 189 – 194 .
  • Tits , A. L. , Absil , P. A. and Woessner , W. P. 2006 . Constraint reduction for linear programs with many inequality constraints . SIAM J. Optim. , 17 : 119 – 146 .
  • Tits , A. L. , W\"achter , A. , Bakhtiari , S. , Urban , T. J. and Lawrence , C. T. 2003 . A primal–dual interior-point method for nonlinear programming with strong global and local convergence properties . SIAM J. Optim. , 14 : 173 – 199 .
  • Tone , K. 1993 . An active-set strategy in an interior point method for linear programming . Math. Program. , 59 : 345 – 360 .
  • Winternitz , L. B. , Nicholls , S. O. , Tits , A. L. and O'Leary , D. P. A constraint-reduced variant of Mehrotra's predictor–corrector algorithm . Comput. Optim. Appl. , (published on-line as of January 2011), DOI: 10.1007/s10589–010–9389–4
  • Wright , S. J. 1997 . Primal–Dual Interior-Point Methods , Philadelphia, PA : SIAM .
  • Ye , Y. 1990 . A `build-down' scheme for linear programming . Math. Program. , 46 : 61 – 72 .

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