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Volumn 77, Issue 2, 1997, Pages 321-333

On the worst case complexity of potential reduction algorithms for linear programming

Author keywords

Interior point methods; Lower bounds on complexity; Potential reduction algorithms

Indexed keywords


EID: 77951500333     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (9)

References (19)
  • 2
    • 84964323821 scopus 로고
    • On the performance of Karmarkar's algorithm over a sequence of iterations
    • K.M. Anstreicher, On the performance of Karmarkar's algorithm over a sequence of iterations, SIAM Journal on Optimization 1 (1991) 22-29.
    • (1991) SIAM Journal on Optimization , vol.1 , pp. 22-29
    • Anstreicher, K.M.1
  • 3
    • 34249927376 scopus 로고
    • Polynomial-time algorithms for linear programming based only on primal scaling and projected gradients of a potential function
    • R. Freund, Polynomial-time algorithms for linear programming based only on primal scaling and projected gradients of a potential function, Mathematical Programming 51 (1991) 203-222.
    • (1991) Mathematical Programming , vol.51 , pp. 203-222
    • Freund, R.1
  • 5
    • 0042407113 scopus 로고
    • An O( √nL)-iteration large-step primal-dual affine algorithm for linear programming
    • C.C. Gonzaga and M.J. Todd, An O( √nL)-iteration large-step primal-dual affine algorithm for linear programming, SIAM Journal on Optimization 2 (1992) 349-359.
    • (1992) SIAM Journal on Optimization , vol.2 , pp. 349-359
    • Gonzaga, C.C.1    Todd, M.J.2
  • 6
    • 30244567410 scopus 로고
    • Convergence behavior of karmarkar's projective algorithm for solving a simple linear program
    • J. Kaliski and Y. Ye, Convergence behavior of Karmarkar's projective algorithm for solving a simple linear program, Operations Research Letters 10 (1991) 389-393.
    • (1991) Operations Research Letters , vol.10 , pp. 389-393
    • Kaliski, J.1    Ye, Y.2
  • 7
    • 51249181779 scopus 로고
    • A new polynomial-time algorithm for linear programming
    • N. Karmarkar (1984), A new polynomial-time algorithm for linear programming, Combinatorica 4 (1991) 373-395.
    • (1984) Combinatorica , vol.4 , pp. 373-395
    • Karmarkar, N.1
  • 8
    • 0026171528 scopus 로고
    • An O( √nL) iteration potential reduction algorithm for linear complementarity problems
    • M. Kojima, S. Mizuno and A. Yoshise, An O( √nL) iteration potential reduction algorithm for linear complementarity problems, Mathematical Programming 50 (1991) 331-342.
    • (1991) Mathematical Programming , vol.50 , pp. 331-342
    • Kojima, M.1    Mizuno, S.2    Yoshise, A.3
  • 9
    • 0347345227 scopus 로고
    • On the improvement per iteration in Karmarkar's algorithm for linear programming
    • C. McDiarmid, On the improvement per iteration in Karmarkar's algorithm for linear programming, Mathematical Programming, 46 (1990) 299-320.
    • (1990) Mathematical Programming , vol.46 , pp. 299-320
    • McDiarmid, C.1
  • 11
    • 0042216624 scopus 로고
    • On the number of iterations of Karmarkar's algorithm for linear programming
    • M.J.D. Powell, On the number of iterations of Karmarkar's algorithm for linear programming, Mathematical Programming 62 (1993) 153-197.
    • (1993) Mathematical Programming , vol.62 , pp. 153-197
    • Powell, M.J.D.1
  • 12
    • 0023862337 scopus 로고
    • A polynomial-time algorithm, based on newton's method, for linear programming
    • J. Renegar, A polynomial-time algorithm, based on Newton's method, for linear programming, Mathematical Programming 40 (1988) 59-93.
    • (1988) Mathematical Programming , vol.40 , pp. 59-93
    • Renegar, J.1
  • 13
    • 0002310026 scopus 로고
    • Centered newton method for mathematical programming
    • M. Iri and K. Yajima, eds., System Modeling and Optimization: Proceedings of the 13th IFIP Conference, Tokyo, Japan, Aug.-Sept. 1987, Springer, Berlin
    • K. Tanabe, Centered Newton method for mathematical programming, in: M. Iri and K. Yajima, eds., System Modeling and Optimization: Proceedings of the 13th IFIP Conference, Tokyo, Japan, Aug.-Sept. 1987, Lecture Notes in Control and Information Sciences 113 (Springer, Berlin, 1988) 197-206.
    • (1988) Lecture Notes in Control and Information Sciences , vol.113 , pp. 197-206
    • Tanabe, K.1
  • 14
    • 0042240298 scopus 로고
    • A lower bound on the number of iterations of primal-dual interior-point methods for linear programming
    • G.A. Watson and D.F. Griffiths, eds., Numerical Analysis 1993, Longman Press, Burnt Hill, UK
    • M.J. Todd, A lower bound on the number of iterations of primal-dual interior-point methods for linear programming, in: G.A. Watson and D.F. Griffiths, eds., Numerical Analysis 1993, Pitman Research Notes in Mathematics 303 (Longman Press, Burnt Hill, UK, 1994) 237-259.
    • (1994) Pitman Research Notes in Mathematics , vol.303 , pp. 237-259
    • Todd, M.J.1
  • 15
    • 0012595684 scopus 로고
    • A centered projective algorithm for linear programming
    • M.J. Todd and Y. Ye, A centered projective algorithm for linear programming, Mathematics of Operations Research 15 (1990) 508-529.
    • (1990) Mathematics of Operations Research , vol.15 , pp. 508-529
    • Todd, M.J.1    Ye, Y.2
  • 16
    • 30244457537 scopus 로고
    • A lower bound on the number of iterations of long-step and polynomial interior-point programming algorithms
    • to appear in
    • M.J. Todd and Y. Ye, A lower bound on the number of iterations of long-step and polynomial interior-point programming algorithms, to appear in Annals of Operations Research (1995).
    • (1995) Annals of Operations Research
    • Todd, M.J.1    Ye, Y.2
  • 17
    • 0025445807 scopus 로고
    • A class of projective transformations for linear programming
    • Y. Ye, A class of projective transformations for linear programming, SIAM Journal on Computing 19 (1990) 457-466.
    • (1990) SIAM Journal on Computing , vol.19 , pp. 457-466
    • Ye, Y.1
  • 18
    • 0026135941 scopus 로고
    • 3L) potential reduction algorithm for linear programming
    • 3L) potential reduction algorithm for linear programming, Mathematical Programming 50 (1991) 239-258.
    • (1991) Mathematical Programming , vol.50 , pp. 239-258
    • Ye, Y.1
  • 19
    • 0041716236 scopus 로고
    • Near boundary behavior of the primal-dual potential reduction algorithm for linear programming
    • Y. Ye, K. Kortanek, J. Kaliski and S. Huang, Near boundary behavior of the primal-dual potential reduction algorithm for linear programming, Mathematical Programming 58 (1993) 243-255.
    • (1993) Mathematical Programming , vol.58 , pp. 243-255
    • Ye, Y.1    Kortanek, K.2    Kaliski, J.3    Huang, S.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.