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Volumn 26, Issue 4, 1997, Pages 1245-1275

Polynomial methods for separable convex optimization in unimodular linear spaces with applications

Author keywords

Min mean canceling; Network flows; Separable convex optimization; Unimodular linear spaces

Indexed keywords

COMBINATORIAL MATHEMATICS; CONVERGENCE OF NUMERICAL METHODS; MATRIX ALGEBRA; OPTIMIZATION; POLYNOMIALS;

EID: 0031209772     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539794263695     Document Type: Article
Times cited : (63)

References (33)
  • 2
    • 43949165470 scopus 로고
    • Two strongly polynomial cut cancelling algorithms for minimum cost network flow
    • T. R. ERVOLINA AND S. T. MCCORMICK, Two strongly polynomial cut cancelling algorithms for minimum cost network flow, Discrete Appl. Math, 46 (1993), pp. 133-165.
    • (1993) Discrete Appl. Math , vol.46 , pp. 133-165
    • Ervolina, T.R.1    Mccormick, S.T.2
  • 3
    • 0020722522 scopus 로고
    • Nonlinear cost network models in transportation analysis
    • M. FLORIAN, Nonlinear cost network models in transportation analysis, Math. Prog. Stud., 26 (1986), pp. 167-196.
    • (1986) Math. Prog. Stud. , vol.26 , pp. 167-196
    • Florian, M.1
  • 5
    • 0024755290 scopus 로고
    • Finding minimum-cost circulations by canceling negative cycles
    • A. V. GOLDBERG AND R. E. TARJAN, Finding minimum-cost circulations by canceling negative cycles, J. Assoc. Comput. Mach., 36 (1989), pp. 873-886.
    • (1989) J. Assoc. Comput. Mach. , vol.36 , pp. 873-886
    • Goldberg, A.V.1    Tarjan, R.E.2
  • 8
    • 0020708796 scopus 로고
    • The minimum cost flow problem: A unifying approach to dual algorithms and a new tree-search algorithm
    • R. HASSIN, The minimum cost flow problem: A unifying approach to dual algorithms and a new tree-search algorithm, Math. Programming, 25 (1983), pp. 228-239.
    • (1983) Math. Programming , vol.25 , pp. 228-239
    • Hassin, R.1
  • 9
    • 85033166523 scopus 로고
    • Working Paper, Department of Statistics and Operations Research, Tel-Aviv University, Tel-Aviv
    • R. HASSIN, A flow algorithm for network synchronization, Working Paper, Department of Statistics and Operations Research, Tel-Aviv University, Tel-Aviv, 1993.
    • (1993) A Flow Algorithm for Network Synchronization
    • Hassin, R.1
  • 10
    • 5244227844 scopus 로고
    • Polynomial and strongly polynomial algorithms for convex network optimization
    • D. Z. Du and P. M. Pardalos, eds., World Scientific, Singapore
    • D. S. HOCHBAUM, Polynomial and strongly polynomial algorithms for convex network optimization, in Network Optimization Problems, D. Z. Du and P. M. Pardalos, eds., World Scientific, Singapore, 1993, pp. 63-92.
    • (1993) Network Optimization Problems , pp. 63-92
    • Hochbaum, D.S.1
  • 11
    • 0025496223 scopus 로고
    • Convex separable optimization is not much harder than linear optimization
    • D. S. HOCHBAUM AND J. G. SHANTHIKUMAR, Convex separable optimization is not much harder than linear optimization, J. Assoc. Comput. Mach., 37 (1990), pp. 843-862.
    • (1990) J. Assoc. Comput. Mach. , vol.37 , pp. 843-862
    • Hochbaum, D.S.1    Shanthikumar, J.G.2
  • 13
    • 0028401018 scopus 로고
    • A new scaling algorithm for the maximum mean cut problem
    • K. IWANO, S. MISONO, S. TEZUKA, AND S. FUJISHIGE, A new scaling algorithm for the maximum mean cut problem, Algorithmica, 11 (1994), pp. 243-255.
    • (1994) Algorithmica , vol.11 , pp. 243-255
    • Iwano, K.1    Misono, S.2    Tezuka, S.3    Fujishige, S.4
  • 14
    • 0001391363 scopus 로고
    • A characterization of the minimum cycle mean in a digraph
    • R. M. KARP, A characterization of the minimum cycle mean in a digraph, Discrete Math., 23 (1978), pp. 309-311.
    • (1978) Discrete Math. , vol.23 , pp. 309-311
    • Karp, R.M.1
  • 15
    • 85033177681 scopus 로고
    • Minimum mean weight cuts and cycles in directed graphs
    • Yaroslavl State University, Yaroslavl, Russia, (in Russian)
    • A. V. KARZANOV, Minimum mean weight cuts and cycles in directed graphs, in Methods for Solving Operator Equations, Yaroslavl State University, Yaroslavl, Russia, 1985, pp. 72-83 (in Russian); Amer. Math. Soc. Transl. (2), 158 (1994), pp. 47-55 (in English).
    • (1985) Methods for Solving Operator Equations , pp. 72-83
    • Karzanov, A.V.1
  • 16
    • 85033174795 scopus 로고
    • in English
    • A. V. KARZANOV, Minimum mean weight cuts and cycles in directed graphs, in Methods for Solving Operator Equations, Yaroslavl State University, Yaroslavl, Russia, 1985, pp. 72-83 (in Russian); Amer. Math. Soc. Transl. (2), 158 (1994), pp. 47-55 (in English).
    • (1994) Amer. Math. Soc. Transl. (2) , vol.158 , pp. 47-55
  • 17
    • 0040610728 scopus 로고
    • Models and algorithms for predicting urban traffic equilibria
    • M. Florian, ed., North-Holland, Amsterdam
    • T. L. MAGNANTI, Models and algorithms for predicting urban traffic equilibria, in Transportation Planning Models, M. Florian, ed., North-Holland, Amsterdam, 1984, pp. 153-186.
    • (1984) Transportation Planning Models , pp. 153-186
    • Magnanti, T.L.1
  • 19
    • 38249000722 scopus 로고
    • Approximate binary search algorithms for mean cuts and cycles
    • S. T. MCCORMICK, Approximate binary search algorithms for mean cuts and cycles, Oper. Res. Lett., 14 (1993), pp. 129-132.
    • (1993) Oper. Res. Lett. , vol.14 , pp. 129-132
    • Mccormick, S.T.1
  • 20
    • 0005497425 scopus 로고
    • An experimental implementation of the dual cancel and tighten algorithm for minimum cost network flow
    • Network Flows and Matching, D. S. Johnson and C. S. McGeoch, eds., AMS, Providence, RI
    • S. T. MCCORMICK AND L. LIU, An experimental implementation of the dual cancel and tighten algorithm for minimum cost network flow, in Network Flows and Matching, D. S. Johnson and C. S. McGeoch, eds., American Mathematical Society DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 12, AMS, Providence, RI, 1993, pp. 247-266.
    • (1993) American Mathematical Society DIMACS Series in Discrete Mathematics and Theoretical Computer Science , vol.12 , pp. 247-266
    • Mccormick, S.T.1    Liu, L.2
  • 22
    • 0001716715 scopus 로고
    • Combinatorial optimization with rational objective functions
    • N. MEGIDDO, Combinatorial optimization with rational objective functions, Math. Oper. Res., 4 (1979), pp. 414-424.
    • (1979) Math. Oper. Res. , vol.4 , pp. 414-424
    • Megiddo, N.1
  • 23
    • 0020828745 scopus 로고
    • Applying parallel computation algorithms in the design of serial algorithms
    • N. MEGIDDO, Applying parallel computation algorithms in the design of serial algorithms, J. Assoc. Comput. Mach., 30 (1983), pp. 852-865.
    • (1983) J. Assoc. Comput. Mach. , vol.30 , pp. 852-865
    • Megiddo, N.1
  • 24
    • 0021608332 scopus 로고
    • A polynomial algorithm for minimum quadratic cost flow problems
    • M. MINOUX, A polynomial algorithm for minimum quadratic cost flow problems, Europ. J. Oper. Res., 18 (1984), pp. 377-387.
    • (1984) Europ. J. Oper. Res. , vol.18 , pp. 377-387
    • Minoux, M.1
  • 25
    • 0020722506 scopus 로고
    • Solving integer minimum cost flows with separable convex cost objective polynomially
    • M. MINOUX, Solving integer minimum cost flows with separable convex cost objective polynomially, Math. Prog. Stud., 26 (1986), pp. 237-239.
    • (1986) Math. Prog. Stud. , vol.26 , pp. 237-239
    • Minoux, M.1
  • 27
    • 0343675970 scopus 로고
    • New scaling algorithms for the assignment and minimum cycle mean problems
    • J. B. ORLIN AND R. K. AHUJA, New scaling algorithms for the assignment and minimum cycle mean problems, Math. Programming, 54 (1988), pp. 41-56.
    • (1988) Math. Programming , vol.54 , pp. 41-56
    • Orlin, J.B.1    Ahuja, R.K.2
  • 28
    • 0003030458 scopus 로고
    • Parametric flows, weighted means of cuts, and fractional combinatorial optimization
    • P. Pardalos, ed., World Scientific, Singapore
    • T. RADZIK, Parametric flows, weighted means of cuts, and fractional combinatorial optimization, in Complexity in Numerical Optimization, P. Pardalos, ed., World Scientific, Singapore, 1993, pp. 351-386.
    • (1993) Complexity in Numerical Optimization , pp. 351-386
    • Radzik, T.1
  • 29
    • 0028399777 scopus 로고
    • Tight bounds on the number of minimum-mean cycle cancellations and related results
    • T. RADZIK AND A. V. GOLDBERG, Tight bounds on the number of minimum-mean cycle cancellations and related results, Algorithmica, 11 (1994), pp. 226-242.
    • (1994) Algorithmica , vol.11 , pp. 226-242
    • Radzik, T.1    Goldberg, A.V.2
  • 30
    • 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
  • 33
    • 0022672734 scopus 로고
    • A strongly polynomial algorithm to solve combinatorial linear programs
    • É. TARDOS, A strongly polynomial algorithm to solve combinatorial linear programs, Oper. Res., 34 (1986), pp. 250-256.
    • (1986) Oper. Res. , vol.34 , pp. 250-256
    • Tardos, É.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.