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Volumn 100, Issue 1, 2004, Pages 133-150

The simplest examples where the simplex method cycles and conditions where EXPAND fails to prevent cycling

Author keywords

Cycling; Degeneracy; EXPAND; Linear programming; Simplex method

Indexed keywords

ALGORITHMS; ERROR ANALYSIS; HEURISTIC METHODS; PERTURBATION TECHNIQUES; PROBLEM SOLVING;

EID: 21044438928     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10107-003-0488-1     Document Type: Review
Times cited : (15)

References (16)
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    • (1963) Recent Advances in Mathematical Programming
    • Balinski, M.L.1    Gomory, R.E.2
  • 2
    • 0000104320 scopus 로고
    • Cycling in the dual simplex algorithm
    • Beale, E.M.L.: Cycling in the dual simplex algorithm. Naval Res. Logistics Quarterly 2, 269-75 (1955)
    • (1955) Naval Res. Logistics Quarterly , vol.2 , pp. 269-275
    • Beale, E.M.L.1
  • 3
    • 38249026962 scopus 로고
    • Degeneracy in the presence of roundoff errors
    • Fletcher, R.: Degeneracy in the presence of roundoff errors. Linear Algebra and its Appl. 106, 149-183 (1988)
    • (1988) Linear Algebra and Its Appl. , vol.106 , pp. 149-183
    • Fletcher, R.1
  • 5
    • 0039545488 scopus 로고
    • Towards reliable linear programming
    • G.A. Watson and D.F. Griffiths, (eds.), Longman Scientific and Technical
    • Fletcher R., Hall, J.A.J.: Towards reliable linear programming. In: G.A. Watson and D.F. Griffiths, (eds.), Pitman Research Notes in Mathematics Series 228, Longman Scientific and Technical, 1990, pp. 89-104
    • (1990) Pitman Research Notes in Mathematics Series 228 , vol.228 , pp. 89-104
    • Fletcher, R.1    Hall, J.A.J.2
  • 6
    • 0012489966 scopus 로고
    • A practical anti-cycling procedure for linearly constrained optimization
    • Gill, P.E., Murray, W., Saunders, M.A., Wright, M.H.: A practical anti-cycling procedure for linearly constrained optimization. Math. Prog. 45, 437-474 (1989)
    • (1989) Math. Prog. , vol.45 , pp. 437-474
    • Gill, P.E.1    Murray, W.2    Saunders, M.A.3    Wright, M.H.4
  • 7
    • 0000726097 scopus 로고
    • A practical steepest-edge simplex algorithm
    • Goldfarb, D., Reid, J.K.: A practical steepest-edge simplex algorithm. Math. Prog. 12, 361-371 (1977)
    • (1977) Math. Prog. , vol.12 , pp. 361-371
    • Goldfarb, D.1    Reid, J.K.2
  • 8
    • 21044436235 scopus 로고    scopus 로고
    • Hyper-sparsity in the revised simplex method and how to exploit it
    • Technical Report MS00-015, Department of Mathematics and Statistics, University of Edinburgh, Submitted to
    • Hall, J.A.J., McKinnon, K.I.M.: Hyper-sparsity in the revised simplex method and how to exploit it. Technical Report MS00-015, Department of Mathematics and Statistics, University of Edinburgh, 2000. Submitted to SIAM Journal of Optimization
    • (2000) SIAM Journal of Optimization
    • Hall, J.A.J.1    McKinnon, K.I.M.2
  • 10
    • 0002825455 scopus 로고
    • Pivot selection methods of the Devex LP code
    • Harris, P.M.J.: Pivot selection methods of the Devex LP code. Math. Prog. 5, 1-28 (1973);
    • (1973) Math. Prog. , vol.5 , pp. 1-28
    • Harris, P.M.J.1
  • 11
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    • [Reprinted in Math. Prog. Study 2, 30-57 (1975)].
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  • 14
    • 0003446306 scopus 로고
    • MINOS 5.4 user's guide
    • Stanford University, Systems Optimization Laboratory, December (revised February 1995)
    • Murtagh, B.A., Saunders, M.A.: MINOS 5.4 user's guide. Technical Report SOL 83-20R, Stanford University, Systems Optimization Laboratory, December 1983 1993. (revised February 1995)
    • (1983) Technical Report , vol.SOL 83-20R
    • Murtagh, B.A.1    Saunders, M.A.2
  • 15
    • 0000238985 scopus 로고
    • A technique for resolving degeneracy in linear programming
    • Wolfe, P.: A technique for resolving degeneracy in linear programming. SIAM J. Appl. Math. 11, 205-211 (1963)
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    • Wolfe, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.