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Volumn 6, Issue 4, 1996, Pages 933-960

Solving LP problems via weighted centers

Author keywords

Linear programming; Newton's method; The ellipsoid method; Weighted center

Indexed keywords


EID: 0030507068     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623493254273     Document Type: Article
Times cited : (1)

References (30)
  • 1
  • 2
    • 0019635237 scopus 로고
    • The ellipsoid method: A survey
    • R. G. BLAND, D. GOLDFARB, AND M. J. TODD, The ellipsoid method: A survey, Oper. Res., 29 (1981), pp. 1039-1091.
    • (1981) Oper. Res. , vol.29 , pp. 1039-1091
    • Bland, R.G.1    Goldfarb, D.2    Todd, M.J.3
  • 3
    • 0022162091 scopus 로고
    • The ellipsoid method generates dual variables
    • B. P. BURRELL AND M. J. TODD, The ellipsoid method generates dual variables, Math. Oper. Res., 10 (1985), pp. 688-700.
    • (1985) Math. Oper. Res. , vol.10 , pp. 688-700
    • Burrell, B.P.1    Todd, M.J.2
  • 4
    • 0004139889 scopus 로고
    • W. H. Freeman and Company, San Francisco, CA
    • V. CHVÁTAL, Linear Programming, W. H. Freeman and Company, San Francisco, CA, 1980.
    • (1980) Linear Programming
    • Chvátal, V.1
  • 5
    • 0019928396 scopus 로고
    • On the non-polynomiality of the relaxation method for systems of linear inequalities
    • J. L. GOFFIN, On the non-polynomiality of the relaxation method for systems of linear inequalities, Math. Programming, 22 (1982), pp. 93-103.
    • (1982) Math. Programming , vol.22 , pp. 93-103
    • Goffin, J.L.1
  • 6
    • 0020132663 scopus 로고
    • Modifications and implementation of the ellipsoid algorithm for linear programming
    • D. GOLDFARB AND M. J. TODD, Modifications and implementation of the ellipsoid algorithm for linear programming, Math. Programming, 23 (1982), pp. 1-19.
    • (1982) Math. Programming , vol.23 , pp. 1-19
    • Goldfarb, D.1    Todd, M.J.2
  • 8
    • 0002940114 scopus 로고
    • Extremum problems with inequalities as subsidiary conditions
    • (Courant Anniversary Volume), Interscience, New York
    • F. JOHN, Extremum problems with inequalities as subsidiary conditions, in Studies and Essays (Courant Anniversary Volume), Interscience, New York, 1948.
    • (1948) Studies and Essays
    • John, F.1
  • 9
    • 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), pp. 373-395.
    • (1984) Combinatorica , vol.4 , pp. 373-395
    • Karmarkar, N.K.1
  • 10
    • 0000769618 scopus 로고
    • A polynomial algorithm for linear programming
    • L. G. KHACHIYAN, A polynomial algorithm for linear programming, Dokl. Akad. Nauk USSR, 244 (1979), pp. 1093-1096.
    • (1979) Dokl. Akad. Nauk USSR , vol.244 , pp. 1093-1096
    • Khachiyan, L.G.1
  • 11
    • 0042778011 scopus 로고
    • On the complexity of approximating the maximal inscribed ellipsoid for a polytope
    • L. G. KHACHIYAN AND M. J. TODD, On the complexity of approximating the maximal inscribed ellipsoid for a polytope, Math. Programming, 61 (1993), pp. 137-159.
    • (1993) Math. Programming , vol.61 , pp. 137-159
    • Khachiyan, L.G.1    Todd, M.J.2
  • 12
    • 0005015952 scopus 로고
    • On an algorithm for the minimization of convex functions
    • A. Y. LEVIN, On an algorithm for the minimization of convex functions, Soviet Math. Dokl., 6 (1965), pp. 286-290.
    • (1965) Soviet Math. Dokl. , vol.6 , pp. 286-290
    • Levin, A.Y.1
  • 14
    • 0027815358 scopus 로고
    • The ellipsoid algorithm using parallel cuts
    • A. LIAO AND M. J. TODD, The ellipsoid algorithm using parallel cuts, Comput. Optim. Appl., 2 (1993), pp. 299-316.
    • (1993) Comput. Optim. Appl. , vol.2 , pp. 299-316
    • Liao, A.1    Todd, M.J.2
  • 15
    • 85033759345 scopus 로고
    • CCOP Report 93-10, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY
    • _, Solving LP Problems via Weighted Centers, CCOP Report 93-10, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY, 1993.
    • (1993) Solving LP Problems Via Weighted Centers
  • 17
    • 84935269021 scopus 로고
    • Pricing criteria in linear programming
    • N. Meggiddo, ed., Springer-Verlag, New York
    • J. L. NAZARETH, Pricing criteria in linear programming, in Progress in Mathematical Programming, N. Meggiddo, ed., Springer-Verlag, New York, 1989, pp. 105-130.
    • (1989) Progress in Mathematical Programming , pp. 105-130
    • Nazareth, J.L.1
  • 18
    • 0040737323 scopus 로고
    • Location of the maximum on unimodal surfaces
    • D. J. NEWMAN, Location of the maximum on unimodal surfaces, J. Assoc. Comput. Mach., 12 (1965), pp. 395-398.
    • (1965) J. Assoc. Comput. Mach. , vol.12 , pp. 395-398
    • Newman, D.J.1
  • 19
    • 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, Math. Programming, 40 (1988), pp. 59-93.
    • (1988) Math. Programming , vol.40 , pp. 59-93
    • Renegar, J.1
  • 20
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton, NJ
    • R. T. ROCKAFELLAR, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 21
    • 0039218959 scopus 로고
    • Utilization of the operation of space dilatation in the minimization of convex functions
    • N. Z. SHOR, Utilization of the operation of space dilatation in the minimization of convex functions, Cybernetics, 6 (1970), pp. 7-15.
    • (1970) Cybernetics , vol.6 , pp. 7-15
    • Shor, N.Z.1
  • 22
    • 0002252730 scopus 로고
    • Cut-off method with space extension in convex programming problems
    • _, Cut-off method with space extension in convex programming problems, Cybernetics, 13 (1977), pp. 94-96.
    • (1977) Cybernetics , vol.13 , pp. 94-96
  • 23
    • 0001292818 scopus 로고
    • An analytical center for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming
    • Springer-Verlag, Berlin
    • G. SONNEVEND, An analytical center for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming, in Lecture Notes in Control and Information Sciences, No. 84, Springer-Verlag, Berlin, 1986, pp. 866-875.
    • (1986) Lecture Notes in Control and Information Sciences , vol.84 , pp. 866-875
    • Sonnevend, G.1
  • 25
    • 0013107819 scopus 로고
    • Technical Report 419, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY
    • M. J. TODD, Some Remarks on the Relaxation Method for Linear Inequalities, Technical Report 419, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY, 1979.
    • (1979) Some Remarks on the Relaxation Method for Linear Inequalities
    • Todd, M.J.1
  • 26
    • 0005664122 scopus 로고
    • On minimum volume ellipsoids containing part of a given ellipsoid
    • _, On minimum volume ellipsoids containing part of a given ellipsoid, Math. Oper. Res., 7 (1980), pp. 253-261.
    • (1980) Math. Oper. Res. , vol.7 , pp. 253-261
  • 27
    • 0009180741 scopus 로고
    • Improved bounds and containing ellipsoids in Karmarkar's linear programming algorithm
    • _, Improved bounds and containing ellipsoids in Karmarkar's linear programming algorithm, Math. Oper. Res., 13 (1988), pp. 650-659.
    • (1988) Math. Oper. Res. , vol.13 , pp. 650-659
  • 28
    • 0001536423 scopus 로고    scopus 로고
    • A new algorithm for minimizing convex functions over convex sets
    • P. M. VAIDYA, A new algorithm for minimizing convex functions over convex sets, Math. Programming, 73 (1996), pp. 291-341.
    • (1996) Math. Programming , vol.73 , pp. 291-341
    • Vaidya, P.M.1
  • 29
    • 0023416760 scopus 로고
    • Karmarkar's algorithm and the ellipsoid method
    • Y. YE, Karmarkar's algorithm and the ellipsoid method, Oper. Res. Lett., 6 (1987), pp. 177-182.
    • (1987) Oper. Res. Lett. , vol.6 , pp. 177-182
    • Ye, Y.1
  • 30
    • 0007639972 scopus 로고
    • Informational complexity and efficient, methods for the solution of convex extremal problems
    • D. B. YUDIN AND A. S. NEMIROVSKII, Informational complexity and efficient, methods for the solution of convex extremal problems, Matekon, 13 (1976), pp. 3-25.
    • (1976) Matekon , vol.13 , pp. 3-25
    • Yudin, D.B.1    Nemirovskii, A.S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.