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Volumn 130, Issue 1, 2001, Pages 1-19

An easy way to teach interior-point methods

Author keywords

Interior point methods; Linear optimization; Polynomial complexity; Self dual embedding; Strictly complementary solution; Strongly polynomial rounding procedure

Indexed keywords


EID: 0008848110     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-2217(00)00094-1     Document Type: Article
Times cited : (12)

References (38)
  • 2
    • 0000728112 scopus 로고    scopus 로고
    • Implementation of interior point methods for large scale linear programming
    • T. Terlaky (Ed.), Kluwer Academic Publishers, Dordrecht, Netherlands
    • E.D. Andersen, J. Gondzio, Cs. Mészâros, X Xu, Implementation of interior point methods for large scale linear programming, in: T. Terlaky (Ed.), Interior Point Methods of Mathematical Programming, Kluwer Academic Publishers, Dordrecht, Netherlands, 1996, pp. 189-252.
    • (1996) Interior Point Methods of Mathematical Programming , pp. 189-252
    • Andersen, E.D.1    Gondzio, J.2    Mészâros, Cs.3    Xu, X.4
  • 4
    • 0003459683 scopus 로고    scopus 로고
    • PhD thesis, Faculty of Technical Mathematics and Computer Science, Delft University of Technology, Delft, Netherlands
    • E. de Klerk, Interior point methods for semidefinite programming. PhD thesis, Faculty of Technical Mathematics and Computer Science, Delft University of Technology, Delft, Netherlands, 1997.
    • (1997) Interior Point Methods for Semidefinite Programming
    • De Klerk, E.1
  • 5
    • 0001624064 scopus 로고    scopus 로고
    • Infeasible-start semidefinite programming algorithms via self-dual embeddings
    • P.M. Pardalos, H. Wolkowicz (Eds.), Fields Institute Communications Series, American Mathematical Society
    • E. de Klerk, C. Roos, and T. Terlaky, Infeasible-start semidefinite programming algorithms via self-dual embeddings, in: P.M. Pardalos, H. Wolkowicz (Eds.), Topics in Semidefinite and Interior-Point Methods, Fields Institute Communications Series, American Mathematical Society, 1998, pp. 215-236.
    • (1998) Topics in Semidefinite and Interior-Point Methods , pp. 215-236
    • De Klerk, E.1    Roos, C.2    Terlaky, T.3
  • 6
    • 0000921195 scopus 로고    scopus 로고
    • Initialization in semidefinite programming via a self-dual skew-symmetric embedding
    • E. de Klerk, C. Roos, T. Terlaky, Initialization in semidefinite programming via a self-dual skew-symmetric embedding, Operations Research Letters 20 (1997) 213-221.
    • (1997) Operations Research Letters , vol.20 , pp. 213-221
    • De Klerk, E.1    Roos, C.2    Terlaky, T.3
  • 7
    • 0039906918 scopus 로고    scopus 로고
    • On primal-dual path-following algorithms for semidefinite programming
    • F. Gianessi, S. Komlósi, T. Rapcsák (Eds.), Kluwer Academic Publishers, Dordrecht, Netherlands
    • E. de Klerk, C. Roos, T. Terlaky, On primal-dual path-following algorithms for semidefinite programming, in: F. Gianessi, S. Komlósi, T. Rapcsák (Eds.), New Trends in Mathematical Programming, Kluwer Academic Publishers, Dordrecht, Netherlands, 1998, pp. 137-157.
    • (1998) New Trends in Mathematical Programming , pp. 137-157
    • De Klerk, E.1    Roos, C.2    Terlaky, T.3
  • 8
    • 0010817129 scopus 로고
    • Technical Report 95-128, Faculty of Technical Mathematics and Computer Science, Delft University of Technology, Delft, Netherlands
    • E. de Klerk, C. Roos, T. Terlaky, Semi-definite problems in truss topology optimization, Technical Report 95-128, Faculty of Technical Mathematics and Computer Science, Delft University of Technology, Delft, Netherlands, 1995.
    • (1995) Semi-definite Problems in Truss Topology Optimization
    • De Klerk, E.1    Roos, C.2    Terlaky, T.3
  • 10
    • 0012126939 scopus 로고
    • SIAM Publications, Philadelphia, PA
    • A.V. Fiacco, G.P. McCormick, Nonlinear Programming: Sequential Unconstrained Minimization Techniques, Wiley, New York, 1968. Reprint: SIAM Classics in Applied Mathematics, vol. 4, SIAM Publications, Philadelphia, PA, pp. 19104-2688, 1990.
    • (1990) SIAM Classics in Applied Mathematics , vol.4 , pp. 19104-22688
  • 12
    • 0003310912 scopus 로고
    • Interior Point Approach to Linear, Quadratic and Convex Programming
    • Kluwer Academic Publishers, Dordrecht, Netherlands
    • D. den Hertog, Interior Point Approach to Linear, Quadratic and Convex Programming, Mathematics and its Applications, vol. 277, Kluwer Academic Publishers, Dordrecht, Netherlands, 1994.
    • (1994) Mathematics and Its Applications , vol.277
    • Den Hertog, D.1
  • 13
    • 0346898360 scopus 로고
    • Interior Point Techniques in Optimization Complexity, Sensitivity and Algorithms
    • Kluwer Academic Publishers, Dordrecht, Netherlands
    • B. Jansen, Interior Point Techniques in Optimization Complexity, Sensitivity and Algorithms, Applied Optimization, vol. 6, Kluwer Academic Publishers, Dordrecht, Netherlands, 1994.
    • (1994) Applied Optimization , vol.6
    • Jansen, B.1
  • 14
    • 0041689097 scopus 로고
    • The theory of linear programming: Skew symmetric self-dual problems and the central path
    • B. Jansen, C. Roos, T. Terlaky, The theory of linear programming: Skew symmetric self-dual problems and the central path, Optimization 29 (1994) 225-233.
    • (1994) Optimization , vol.29 , pp. 225-233
    • Jansen, B.1    Roos, C.2    Terlaky, T.3
  • 16
    • 51249181779 scopus 로고
    • A new polynomial-time algorithm for linear programming
    • N.K. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica 4 (1984) 373-395.
    • (1984) Combinatorica , vol.4 , pp. 373-395
    • Karmarkar, N.K.1
  • 17
    • 0002431411 scopus 로고
    • Animplementation of a primal-dual interior point method for linear programming
    • K.A. McShane, C.L. Monma, D.F. Shanno, Animplementation of a primal-dual interior point method for linear programming, ORSA Journal on Computing 1 (1989) 70-83.
    • (1989) ORSA Journal on Computing , vol.1 , pp. 70-83
    • McShane, K.A.1    Monma, C.L.2    Shanno, D.F.3
  • 18
    • 0001961709 scopus 로고
    • Pathways to the optimal set inlinear programming
    • N. Megiddo (Ed.), Springer, New York
    • N. Megiddo. Pathways to the optimal set inlinear programming, in: N. Megiddo (Ed.), Progress in Mathematical Programming: Interior Point and Related Methods, Springer, New York, 1989, pp. 131-158. Identical version in: Proceedings of the Sixth Mathematical Programming Symposium of Japan, Nagoya, Japan, 1986, pp. 1-35.
    • (1989) Progress in Mathematical Programming: Interior Point and Related Methods , pp. 131-158
    • Megiddo, N.1
  • 19
    • 0346267935 scopus 로고
    • Nagoya, Japan
    • N. Megiddo. Pathways to the optimal set inlinear programming, in: N. Megiddo (Ed.), Progress in Mathematical Programming: Interior Point and Related Methods, Springer, New York, 1989, pp. 131-158. Identical version in: Proceedings of the Sixth Mathematical Programming Symposium of Japan, Nagoya, Japan, 1986, pp. 1-35.
    • (1986) Proceedings of the Sixth Mathematical Programming Symposium of Japan , pp. 1-35
  • 20
    • 0000561116 scopus 로고
    • On the implementation of a (primal-dual) interior point method
    • S. Mehrotra, On the implementation of a (primal-dual) interior point method, SIAM Journal on Optimization 2 (4) (1992) 575-601.
    • (1992) SIAM Journal on Optimization , vol.2 , Issue.4 , pp. 575-601
    • Mehrotra, S.1
  • 21
    • 34250077538 scopus 로고
    • On finding the optimal facet of linear programs
    • S. Mehrotra, Y. Ye, On finding the optimal facet of linear programs, Mathematical Programming 62 (1993) 497-515.
    • (1993) Mathematical Programming , vol.62 , pp. 497-515
    • Mehrotra, S.1    Ye, Y.2
  • 22
    • 0002760301 scopus 로고    scopus 로고
    • A general parametric analysis approach and its implications to sensitivity analysis in interior point methods
    • R.D.C. Monteiro, S. Mehrotra, A general parametric analysis approach and its implications to sensitivity analysis in interior point methods, Mathematical Programming 72 (1996) 65-82.
    • (1996) Mathematical Programming , vol.72 , pp. 65-82
    • Monteiro, R.D.C.1    Mehrotra, S.2
  • 24
    • 0031073753 scopus 로고    scopus 로고
    • Self-scaled barriers and interior-point methods for convex programming
    • Y.E. Nesterov, M.J. Todd, Self-scaled barriers and interior-point methods for convex programming, Mathematics of Operations Research 22 (1) (1997) 1-42.
    • (1997) Mathematics of Operations Research , vol.22 , Issue.1 , pp. 1-42
    • Nesterov, Y.E.1    Todd, M.J.2
  • 25
    • 0007159786 scopus 로고    scopus 로고
    • Technical Report 98-05, Faculty of Technical Mathematics and Computer Science, Delft University of Technology, Delft, Netherlands, Annals of Operations Research (to appear)
    • J. Peng, C. Roos, T. Terlaky, New complexity analysis of the primal-dual Newton method for linear optimization, Technical Report 98-05, Faculty of Technical Mathematics and Computer Science, Delft University of Technology, Delft, Netherlands, 1998, Annals of Operations Research (to appear).
    • (1998) New Complexity Analysis of the Primal-dual Newton Method for Linear Optimization
    • Peng, J.1    Roos, C.2    Terlaky, T.3
  • 26
    • 0039545608 scopus 로고
    • Homogeneous interior point algorithms for semidefinite programming
    • Department of Mathematics, The University of Iowa, Iowa City, IA
    • F.A. Potra, R. Sheng, Homogeneous interior point algorithms for semidefinite programming, Reports on Computational Mathematics 82, Department of Mathematics, The University of Iowa, Iowa City, IA, 1995.
    • (1995) Reports on Computational Mathematics , vol.82
    • Potra, F.A.1    Sheng, R.2
  • 27
    • 0003495411 scopus 로고    scopus 로고
    • Theory and Algorithms for Linear Optimization
    • Wiley, Chichester, UK
    • C. Roos, T. Terlaky, J.-Ph.Vial, Theory and Algorithms for Linear Optimization, An Interior Approach, Wiley, Chichester, UK, 1997.
    • (1997) An Interior Approach
    • Roos, C.1    Terlaky, T.2    Vial, J.-Ph.3
  • 28
    • 0001292818 scopus 로고
    • An analytic center for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming
    • A. Prékopa, J. Szelezsán, B. Strazicky, (Eds.), Budapest, Hungary, September
    • G. Sonnevend, An analytic center for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming, in: A. Prékopa, J. Szelezsán, B. Strazicky, (Eds.), System Modeling and Optimization: Proceedings of the 12th IFIP-Conference, Budapest, Hungary, September 1985, Lecture Notes in Control and Information Sciences, vol. 84, Springer, Berlin, 1986, pp. 866-876.
    • (1985) System Modeling and Optimization: Proceedings of the 12th IFIP-Conference
    • Sonnevend, G.1
  • 29
    • 0004050029 scopus 로고
    • Springer, Berlin
    • G. Sonnevend, An analytic center for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming, in: A. Prékopa, J. Szelezsán, B. Strazicky, (Eds.), System Modeling and Optimization: Proceedings of the 12th IFIP-Conference, Budapest, Hungary, September 1985, Lecture Notes in Control and Information Sciences, vol. 84, Springer, Berlin, 1986, pp. 866-876.
    • (1986) Lecture Notes in Control and Information Sciences , vol.84 , pp. 866-876
  • 31
    • 0346898359 scopus 로고    scopus 로고
    • Interior Point Methods of Mathematical Programming
    • Kluwer Academic Publishers, Dordrecht, Netherlands
    • T. Terlaky (Ed.), Interior Point Methods of Mathematical Programming, Applied Optimization, vol. 5, Kluwer Academic Publishers, Dordrecht, Netherlands, 1996.
    • (1996) Applied Optimization , vol.5
    • Terlaky, T.1
  • 32
    • 0001768599 scopus 로고
    • Dual systems of homogeneous linear relations
    • H.W. Kuhn, A.W. Tucker (Eds.), Princeton University Press, Princeton, NJ
    • A.W. Tucker. Dual systems of homogeneous linear relations, in: H.W. Kuhn, A.W. Tucker (Eds.), Linear Inequalities and Related Systems, Annals of Mathematical Studies, vol. 38, Princeton University Press, Princeton, NJ, 1956, pp. 3-18.
    • (1956) Linear Inequalities and Related Systems, Annals of Mathematical Studies , vol.38 , pp. 3-18
    • Tucker, A.W.1
  • 33
    • 0030106462 scopus 로고    scopus 로고
    • Semidefinite programming
    • L. Vandenberghe, S. Boyd, Semidefinite programming, SIAM Review 38 (1996) 49-95.
    • (1996) SIAM Review , vol.38 , pp. 49-95
    • Vandenberghe, L.1    Boyd, S.2
  • 36
    • 30244459714 scopus 로고
    • On the finite convergence of interior-point algorithms for linear programming
    • Y. Ye, On the finite convergence of interior-point algorithms for linear programming, Mathematical Programming 57 (1992) 325-335.
    • (1992) Mathematical Programming , vol.57 , pp. 325-335
    • Ye, Y.1
  • 37
    • 0004212716 scopus 로고    scopus 로고
    • Interior Point Algorithms
    • Wiley, Chichester, UK
    • Y. Ye, Interior Point Algorithms, Theory and Analysis, Wiley, Chichester, UK, 1997.
    • (1997) Theory and Analysis
    • Ye, Y.1
  • 38
    • 0003058678 scopus 로고
    • An O(√nL)-iteration homogeneous and self-dual linear programming algorithm
    • Y. Ye, M.J. Todd, S. Mizuno, An O(√nL)-iteration homogeneous and self-dual linear programming algorithm, Mathematics of Operations Research 19 (1994) 53-67.
    • (1994) Mathematics of Operations Research , vol.19 , pp. 53-67
    • Ye, Y.1    Todd, M.J.2    Mizuno, S.3


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