An infeasible-interior-point method for the P(k) -matrix LCP

Authors

  • Jun Ji Valdosta State University, USA
  • Florian A. Potra University of Iowa, USA
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References

J. F. Bonnans and C. C. Gonzaga, Convergence of interior point algorithms for the monotone linear complementarity problerm, Mathematics of Operations Research 21, I (1996), pp.1-25, https://doi.org/10.1287/moor.21.1.1

R M. Freund, An Infeasible-start Algorithm for Linear Programming Wose Complexity Depends on the Distance from the Starting Point to the Optimal Solution, Working Paper 3559-93-MSA, Sloan School of Management, Massachusetts lnstitute of Technology, Cambridge, MA 02139, USA, 1993.

O. Güler, Generalized linear complementarity problems, Mathematics of Operations Research 20, 2 (1995), pp. 441-448, https://doi.org/10.1287/moor.20.2.441

A. J. Hoffman, On approximate solutions of systems of linear inequalities, Journal of Research of the National Bureau of Standards 49, (1952), pp. 263 -265, https://doi.org/10.6028/jres.049.027

J. Ji and F. A. Potra, On the Average Complexity of Finding an ε-Optimal Solution for Linear Programming, Reports on Computational Mathematics 25, Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA, (1992).

J. Ji, F. A. Potra and S. Huang, A predictor-corrector method for linear complementarity problems with polynomial complexity and superlinear convergence. Journal of Optimization Theory and Applications 85, (1995), pp. 187-199, https://doi.org/10.1007/bf02192304

M. Kojima, N. Megiddo, T. Noma and A. Yoshise, A Unified Approach to Interior point Algorithms for Linear Complementarity Problems, Lecture Notes in Comput. Sci., 538, Springer Verlag, New York, 1991, https://doi.org/10.1007/3-540-54509-3

M. Kojima, N. Megiddo, and S. Mizruro, A primal-dual infeasible-interior-point algorithm for Iinear programming, Mathematical programming, 61, (1993 ), 263-280, https://doi.org/10.1007/bf01582151

M. Kojima, S. Mizuno and M. J. Todd,Infeasible-interior-point primal-dual potential-reduction algorithms for linear programning, SIAM J. Oprimization 5, 1 (1995), pp. 52-67, https://doi.org/10.1137/0805003

J. Lustig, R. E. Marsten and D. F. Shanno, Computational experience with a globally convergent primal-dual predictor-corrector algorithm for Iinear programming,Mathematical Programming 66 (1994), pp. 123-135, https://doi.org/10.1007/bf01581140

J. Miao, A quadratically convergent O((1+k)√(nL) -iteration algorithm for the P_{∗}(k)-matrix Iinear complementarity problem, Mathematical programming 69, (1995), pp. 355-369, https://doi.org/10.1007/bf01585565

J. Miao, Two infeasible interior-point predictor-corrector algorithms for linear programming, SIAM J, Optimization 6, 3 (1996), pp. 587-599, https://doi.org/10.1137/s105262349325771x

S. Mizuno, Polynomiality of infeasible-interior-point algorithm for linear programming, Mathematical Programming 67, 1 (1994), pp. 109.

S. Mizuno, M. J. Todd and Y. Ye, On adaptive-stuep primal-dual interior-point algorithms for linear programming, Mathematics of Operations Research 128, 4 (1993), pp. 964-981.

R.D.C. Monteiro and S.J. Wright, Local convergence of interior-point algorithm for degenerate montone LCP, Computational Optimization and Applications, 3 (1994), pp. 131-155.

R.D.C. Monteiro and S.J. Wright, Superlinear primal-dual affine scaling algorithms for LCP, SIAM J. Optimization 6, 1 (1996), pp. 1-18.

A.M. Ostrowski, Solution of Equations in Euclidean and Banach Spaces, Academic Press, New York, (1973).

F. A. Potra, An infeasible interior-point predictor-corrector algorithm for linear programming, SIAM J. Optimizaiton 6, 1 (1996), pp. 19-32.

F. A. Potra, A quadratically convergent predictor-corrector method for solving linear programs from infeasible starting points, Mathematical Programming 67, (1994), pp. 383-406.

F. A. Potra, An O(nl) infeasible interior-point algorithm for LCP with quadratic convergence, Annals of Operations Research 62, (1996), pp. 81-102.

R. H. Tütüncü and M. J.. Todd, Reducing Horizontal Linear Complementarity Problems, Technical Report 1023, School of Operations Research and Industrial Engineering, Cornell Univeristy, Ithaca, NY 14853-3801, USA (1992).

F. Wu, S. and Y. Ye, On Quadratic Convergence of the Homogeneous and Self-dual Linear Programming Algorithm, Working Paner, Department of Management Sciences, The University of Iowa, Iowa City, IA52242, USA (1993).

S. J. Wright, an infeasible-interior-point algorithm for linear complementarity problems, Mathematical Programming 67, 1 (1994), pp. 29-52.

S. Wright, A path-following infeasible-interior-point algorithm for linear compplementarity problems, Optimizaiton Methods and Software 2 (1993), pp. 79-196.

Y. Ye and K. Anstreicher, On quadratic and O(√(nL)) convergence of predictor-corrector algorithm for LCp, Mathematical Programming 62, 3 (1993), pp. 537-551.

Y. Ye, O. Güler, R. A. Tapia and Y. Zhang, A quadratically convergent of O(√(Ln))-iteration algorithm for linear programming, Mathematical Programming 59, 2 (1993), pp. 151-162.

Y. Ye, M. J. Todd and S. Mizuno, An O(√(Ln)) -iteration homogeneous and self-dual linear programming algorithm, Mathematics of Operations Research 19, 1 (1994), pp. 53-67.

Y. Zhang, On the convergence of a class of infeasible interior-point methods for the horizontal linear complementarity problem, SIAM J. Optimizaiton 4,1 (1994), pp. 208-227.

Y. Zhang and D. Zhang, Superlinear convergence of infeasible interior-point methods for linear programming, Mathematical Programming 66, 3 (1994), pp.361-378

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1998-08-01

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Ji, J., & Potra, F. A. (1998). An infeasible-interior-point method for the P(k) -matrix LCP. Rev. Anal. Numér. Théor. Approx., 27(2), 277-295. https://ictp.acad.ro/jnaat/journal/article/view/1998-vol27-no2-art9