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Volumn 17, Issue 5, 1996, Pages 1202-1223

An investigation of interior-point algorithms for the linear transportation problem

Author keywords

Interior point algorithms; Large scale problems; Linear transportation models; Preconditioned conjugate gradient methods

Indexed keywords


EID: 0000995669     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827593258280     Document Type: Article
Times cited : (12)

References (39)
  • 1
    • 0001844689 scopus 로고
    • Data structures and programming techniques for the implementation of Karmarkar's algorithm
    • I. ADLER, N. KARMARKAR, M. RESENDE, AND G. VEIGA, Data structures and programming techniques for the implementation of Karmarkar's algorithm, ORSA J. Comput., 1 (1989), pp. 84-106.
    • (1989) ORSA J. Comput. , vol.1 , pp. 84-106
    • Adler, I.1    Karmarkar, N.2    Resende, M.3    Veiga, G.4
  • 2
    • 0026119751 scopus 로고
    • Limiting behavior of the affine scaling continuous trajectories for linear programming problems
    • I. ADLER AND R. MONTEIRO, Limiting behavior of the affine scaling continuous trajectories for linear programming problems, Math. Programming, 50 (1989), pp. 29-51.
    • (1989) Math. Programming , vol.50 , pp. 29-51
    • Adler, I.1    Monteiro, R.2
  • 3
    • 0000110392 scopus 로고
    • An implementation of Karmarkar's algorithm for linear programming
    • I. ADLER, M. RESENDE, G. VEIGA, AND N. KARMARKAR, An implementation of Karmarkar's algorithm for linear programming, Math. Programming, 44 (1989), pp. 297-335.
    • (1989) Math. Programming , vol.44 , pp. 297-335
    • Adler, I.1    Resende, M.2    Veiga, G.3    Karmarkar, N.4
  • 5
    • 0022808141 scopus 로고
    • A variation on Karmarkar's algorithm for solving linear programming problems
    • E. BARNES, A variation on Karmarkar's algorithm for solving linear programming problems, Math. Programming, 36 (1986), pp. 174-182.
    • (1986) Math. Programming , vol.36 , pp. 174-182
    • Barnes, E.1
  • 6
    • 0026923017 scopus 로고
    • Very large-scale linear programming: A case study in combining interior point and simplex methods
    • R. BIXBY, J. GREGORY, I. LUSTIG, R. MARSTEN, AND D. SHANNO, Very large-scale linear programming: A case study in combining interior point and simplex methods, Oper. Res., 40 (1992), pp. 885-897.
    • (1992) Oper. Res. , vol.40 , pp. 885-897
    • Bixby, R.1    Gregory, J.2    Lustig, I.3    Marsten, R.4    Shanno, D.5
  • 8
    • 0000754239 scopus 로고
    • Iterative solution of problems of linear and quadratic programming
    • I. DIKIN, Iterative solution of problems of linear and quadratic programming, Soviet Math. Dokl., 8 (1967), pp. 674-675.
    • (1967) Soviet Math. Dokl. , vol.8 , pp. 674-675
    • Dikin, I.1
  • 10
    • 0004236492 scopus 로고
    • The Johns Hopkins University Press, Baltimore, MD
    • G. GOLUB AND C. V. LOAN, Matrix Computations, The Johns Hopkins University Press, Baltimore, MD, 1983.
    • (1983) Matrix Computations
    • Golub, G.1    Loan, C.V.2
  • 11
    • 0038958900 scopus 로고
    • Two-Third is Sharp for Affine Scaling
    • Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ
    • L. HALL AND R. VANDERBEI, Two-Third is Sharp for Affine Scaling, Tech. report, Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ, 1992.
    • (1992) Tech. Report
    • Hall, L.1    Vanderbei, R.2
  • 12
    • 0028530911 scopus 로고
    • Primal-dual algorithms for linear programming based on the logarithmic barrier method
    • B. JANSEN, C. ROOS, T. TERLAKY, AND J. VIAL, Primal-dual algorithms for linear programming based on the logarithmic barrier method, J. Optim. Theory Appl., 83 (1994), pp. 1-26.
    • (1994) J. Optim. Theory Appl. , vol.83 , pp. 1-26
    • Jansen, B.1    Roos, C.2    Terlaky, T.3    Vial, J.4
  • 13
    • 0002379820 scopus 로고
    • A fast implementation of a path-following algorithm for maximizing a linear function over a network polytope
    • D. Johnson and C. McGeoch, eds., American Mathematical Society, Providence, RI
    • A. JOSHI, S. GOLDSTEIN, AND P. VAIDYA, A fast implementation of a path-following algorithm for maximizing a linear function over a network polytope, in Network Flows and Matching: First DIMACS Implementation Challenge, D. Johnson and C. McGeoch, eds., American Mathematical Society, Providence, RI, 1993, pp. 267-298.
    • (1993) Network Flows and Matching: First DIMACS Implementation Challenge , pp. 267-298
    • Joshi, A.1    Goldstein, S.2    Vaidya, P.3
  • 14
    • 0027617194 scopus 로고
    • A decomposition variant of the potential reduction algorithm for linear programming
    • J. KALISKI AND Y. YE, A decomposition variant of the potential reduction algorithm for linear programming, Management Sci., 39 (1993), pp. 757-776.
    • (1993) Management Sci. , vol.39 , pp. 757-776
    • Kaliski, J.1    Ye, Y.2
  • 15
    • 51249181779 scopus 로고
    • A new polynomial-time algorithm for linear programming
    • N. KARMARKAR, A new polynomial-time algorithm for linear programming, Combinatorica, 4 (1984), pp. 373-395.
    • (1984) Combinatorica , vol.4 , pp. 373-395
    • Karmarkar, N.1
  • 17
    • 0015989127 scopus 로고
    • Netgen: A program for generating large scale capacitated assignment, transportation and minimum cost flow network problems
    • D. KLINGMAN, A. NAPIER, AND J. STUTZ, Netgen: A program for generating large scale capacitated assignment, transportation and minimum cost flow network problems. Management Sci., 20 (1974), pp. 814-821.
    • (1974) Management Sci. , vol.20 , pp. 814-821
    • Klingman, D.1    Napier, A.2    Stutz, J.3
  • 19
    • 0026171528 scopus 로고
    • An O(√nl) iteration potential reduction algorithm for linear complementarity problems
    • _, An O(√nl) iteration potential reduction algorithm for linear complementarity problems, Math. Programming, 50 (1991), pp. 331-342.
    • (1991) Math. Programming , vol.50 , pp. 331-342
  • 20
    • 85033856820 scopus 로고
    • SIAG/OPT Views-and-News, a forum for the SIAM Activity Group on Optimization
    • Philadelphia, PA
    • E. KRANICH, SIAG/OPT Views-and-News, a forum for the SIAM Activity Group on Optimization, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992.
    • (1992) Society for Industrial and Applied Mathematics
    • Kranich, E.1
  • 21
  • 22
    • 85033834067 scopus 로고
    • Philadelphia, PA
    • I. LUSTIG, R. MARSTEN, AND D. SHANNO, The primal-dual interior point method on the Cray supercomputer, in Large-Scale Numerical Optimization, SIAM Proc. in Applied Mathematics, Ithaca, NY, 1989, T. Coleman and Y. Li, eds., Society for Industrial and Applied Mathematics, Philadelphia, PA, 1990, pp. 70-80.
    • (1990) Society for Industrial and Applied Mathematics , pp. 70-80
    • Coleman, T.1    Li, Y.2
  • 23
    • 0041507266 scopus 로고
    • Interior method vs. simplex method: Beyond netlib
    • _, Interior method vs. simplex method: Beyond netlib, COAL Newsletter, 19 (1991), pp. 41-44.
    • (1991) COAL Newsletter , vol.19 , pp. 41-44
  • 24
    • 0000022796 scopus 로고
    • On implementing Mehrotra's predictor-corrector interior-point method for linear programming
    • _, On implementing Mehrotra's predictor-corrector interior-point method for linear programming, SIAM J. Optim., 2 (1992), pp. 435-449.
    • (1992) SIAM J. Optim. , vol.2 , pp. 435-449
  • 25
    • 0001662422 scopus 로고
    • Interior methods: Computational state of the art
    • _, Interior methods: Computational state of the art, ORSA J. Computing, 6 (1994), pp. 1-14.
    • (1994) ORSA J. Computing , vol.6 , pp. 1-14
  • 26
    • 0042746125 scopus 로고
    • Implementation of a dual affine interior point algorithm for linear programming
    • R. MARSTEN, M. SALTZMAN, D. SHANNO, G. PIERCE, AND J. BALLINTUN, Implementation of a dual affine interior point algorithm for linear programming, ORSA J. Comput., 1 (1989), pp. 287-297.
    • (1989) ORSA J. Comput. , vol.1 , pp. 287-297
    • Marsten, R.1    Saltzman, M.2    Shanno, D.3    Pierce, G.4    Ballintun, J.5
  • 27
    • 0002431411 scopus 로고
    • An implementation of a primal-dual interior-point method for linear programming
    • K. MCSHANE, C. MONMA, AND D. SHANNO, An implementation of a primal-dual interior-point method for linear programming, ORSA J. Comput., 1 (1989), pp. 70-83.
    • (1989) ORSA J. Comput. , vol.1 , pp. 70-83
    • McShane, K.1    Monma, C.2    Shanno, D.3
  • 28
    • 0011372565 scopus 로고
    • On the Implementation of a (Primal-Dual) Interior-Point Method
    • Department of Industrial Engineering and Management Science, Northwestern University, Evanston, IL
    • S. MEHROTRA, On the Implementation of a (Primal-Dual) Interior-Point Method, Tech. report 90-03, Department of Industrial Engineering and Management Science, Northwestern University, Evanston, IL, 1990.
    • (1990) Tech. Report 90-03
    • Mehrotra, S.1
  • 29
    • 0023591611 scopus 로고
    • Computational experience with a dual affine variant of Karmarkar's method for linear programming
    • C. MONMA AND A. MORTON, Computational experience with a dual affine variant of Karmarkar's method for linear programming, Oper. Res. Lett., 6 (1987), pp. 177-182.
    • (1987) Oper. Res. Lett. , vol.6 , pp. 177-182
    • Monma, C.1    Morton, A.2
  • 30
    • 0024665752 scopus 로고
    • Interior path following primal-dual algorithms. Part I: Linear programming
    • R. MONTEIRO AND I. ADLER, Interior path following primal-dual algorithms. Part I: Linear programming, Math. Programming, 44 (1989), pp. 27-41.
    • (1989) Math. Programming , vol.44 , pp. 27-41
    • Monteiro, R.1    Adler, I.2
  • 31
    • 0000783956 scopus 로고
    • A polynomial-time primal-dual affine scaling algorithm for linear and convex quadratic programming and its power series extension
    • R. MONTEIRO, I. ADLER, AND M. RESENDE, A polynomial-time primal-dual affine scaling algorithm for linear and convex quadratic programming and its power series extension, Math. Oper. Res., 15 (1990), pp. 191-214.
    • (1990) Math. Oper. Res. , vol.15 , pp. 191-214
    • Monteiro, R.1    Adler, I.2    Resende, M.3
  • 32
    • 28844479928 scopus 로고
    • A convergence analysis of a long-step variant of the projective scaling algorithm
    • The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-Ku, Tokyo 106, Japan
    • M. MURAMATSU AND T. TSUCHIYA, A convergence analysis of a long-step variant of the projective scaling algorithm, Research memorandum, The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-Ku, Tokyo 106, Japan, 1992.
    • (1992) Research Memorandum
    • Muramatsu, M.1    Tsuchiya, T.2
  • 34
    • 0002383010 scopus 로고
    • Identifying the optimal face of a network linear program with a globally convergent interior point method
    • H. Hager, D. Hearn, and P. Pardalos, eds., Kluwer Academic Publishers, Norwell, MA
    • M. RESENDE, T. TSUCHIYA, AND G. VEIGA, Identifying the optimal face of a network linear program with a globally convergent interior point method, in Large Scale Optimization: State of the Art, H. Hager, D. Hearn, and P. Pardalos, eds., Kluwer Academic Publishers, Norwell, MA, 1994, pp. 362-386.
    • (1994) Large Scale Optimization: State of the Art , pp. 362-386
    • Resende, M.1    Tsuchiya, T.2    Veiga, G.3
  • 35
    • 0001024483 scopus 로고
    • An efficient implementation of a network interior point method
    • D. Johnson and C. McGeoch, eds., American Mathematical Society, Providence, RI
    • M. RESENDE AND G. VEIGA, An efficient implementation of a network interior point method, in Networks Flow and Matching: First DIMACS Implementation Challenge, Vol. 12, D. Johnson and C. McGeoch, eds., American Mathematical Society, Providence, RI, 1993, pp. 299-384.
    • (1993) Networks Flow and Matching: First DIMACS Implementation Challenge , vol.12 , pp. 299-384
    • Resende, M.1    Veiga, G.2
  • 36
    • 0001157796 scopus 로고
    • An implementation of the dual affine scaling algorithm for minimum-cost flow on bipartite uncapacitated networks
    • _, An implementation of the dual affine scaling algorithm for minimum-cost flow on bipartite uncapacitated networks, SIAM J. Optim., 3 (1993), pp. 516-537.
    • (1993) SIAM J. Optim. , vol.3 , pp. 516-537
  • 38
    • 0022956879 scopus 로고
    • A modification of Karmarkar's linear programming algorithm
    • R. VANDERBEI, M. MEKETON, AND B. FREEDMAN, A modification of Karmarkar's linear programming algorithm, Algorithmica, 1 (1986), pp. 395-407.
    • (1986) Algorithmica , vol.1 , pp. 395-407
    • Vanderbei, R.1    Meketon, M.2    Freedman, B.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.