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Volumn 121, Issue 1, 2004, Pages 19-39

On the global optimization of sums of linear fractional functions over a convex set

Author keywords

Concave minimization; Global optimization; Linear fractional functions; Parametric programming; Sum of ratios

Indexed keywords

CONVEX OPTIMIZATION; FUNCTIONS; PROBLEM SOLVING; SET THEORY;

EID: 4043135727     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JOTA.0000026129.07165.5a     Document Type: Article
Times cited : (79)

References (30)
  • 1
    • 0000042501 scopus 로고
    • A note on the sum of a linear and linear-fractional function
    • SCHAIBLE, S., A Note on the Sum of a Linear and Linear-Fractional Function, Naval Research Logistics Quarterly, Vol. 24, pp. 691-693, 1977.
    • (1977) Naval Research Logistics Quarterly , vol.24 , pp. 691-693
    • Schaible, S.1
  • 2
    • 0006761690 scopus 로고
    • Parametric analysis of a multistage stochastic shipping problem
    • Edited by J. Lawrence, Tavistock Publications, London, England
    • ALMOGY, Y., and LEVIN, O., Parametric Analysis of a Multistage Stochastic Shipping Problem, Operational Research 69, Edited by J. Lawrence, Tavistock Publications, London, England, 1970.
    • (1970) Operational Research 69
    • Almogy, Y.1    Levin, O.2
  • 3
    • 0002168842 scopus 로고
    • Optimizing the sum of linear fractional functions
    • Edited by C. A. Floudas, and P. M. Pardalos, Princeton University Press, Princeton, New Jersey
    • FALK, J. E., and PALOCSAY, S. W., Optimizing the Sum of Linear Fractional Functions, Recent Advances in Global Optimization, Edited by C. A. Floudas, and P. M. Pardalos, Princeton University Press, Princeton, New Jersey, 1992.
    • (1992) Recent Advances in Global Optimization
    • Falk, J.E.1    Palocsay, S.W.2
  • 4
    • 0006840716 scopus 로고
    • Programming, profit rates, and pricing decisions
    • COLANTONI, C. S., MANES, R. P., and WHINSTON, A., Programming, Profit Rates, and Pricing Decisions, Accounting Review, Vol. 44, pp. 467-481, 1969.
    • (1969) Accounting Review , vol.44 , pp. 467-481
    • Colantoni, C.S.1    Manes, R.P.2    Whinston, A.3
  • 6
    • 0001404993 scopus 로고    scopus 로고
    • Bond portfolio optimization problems and their applications to index tracking: A partial optimization approach
    • KONNO, H., and WATANABE, H., Bond Portfolio Optimization Problems and Their Applications to Index Tracking: A Partial Optimization Approach, Journal of the Operations Research Society of Japan, Vol. 39, pp. 295-306, 1996.
    • (1996) Journal of the Operations Research Society of Japan , vol.39 , pp. 295-306
    • Konno, H.1    Watanabe, H.2
  • 8
    • 0002398911 scopus 로고
    • Parametric simplex algorithms for solving a special class of nonconvex minimization problems
    • KONNO, H., YAJIMA, Y., and MATSUI, T., Parametric Simplex Algorithms for Solving a Special Class of Nonconvex Minimization Problems, Journal of Global Optimization, Vol. 1, pp. 65-81, 1991.
    • (1991) Journal of Global Optimization , vol.1 , pp. 65-81
    • Konno, H.1    Yajima, Y.2    Matsui, T.3
  • 9
    • 0003136739 scopus 로고
    • Image space analysis of generalized fractional programs
    • FALK, J. E., and PALOCSAY, S. W., Image Space Analysis of Generalized Fractional Programs, Journal of Global Optimization, Vol. 4, pp. 63-88, 1994.
    • (1994) Journal of Global Optimization , vol.4 , pp. 63-88
    • Falk, J.E.1    Palocsay, S.W.2
  • 10
    • 0006796190 scopus 로고
    • Global minimization of a generalized convex multiplicative function
    • KONNO, H., KUNO, T., and YAJIMA, Y., Global Minimization of a Generalized Convex Multiplicative Function, Journal of Global Optimization, Vol. 4, pp. 47-62, 1994.
    • (1994) Journal of Global Optimization , vol.4 , pp. 47-62
    • Konno, H.1    Kuno, T.2    Yajima, Y.3
  • 11
    • 0002148307 scopus 로고
    • Concave minimization: Theory, applications, and algorithms
    • Edited by R. Horst and P. M. Pardalos, Kluwer Academic Publishers, Dordrecht, Netherlands
    • BENSON, H. P., Concave Minimization: Theory, Applications, and Algorithms, Handbook of Global Optimization, Edited by R. Horst and P. M. Pardalos, Kluwer Academic Publishers, Dordrecht, Netherlands, 1995.
    • (1995) Handbook of Global Optimization
    • Benson, H.P.1
  • 12
    • 0030242902 scopus 로고    scopus 로고
    • Deterministic algorithms for constrained concave minimization: A unified critical survey
    • BENSON, H. P., Deterministic Algorithms for Constrained Concave Minimization: A Unified Critical Survey, Naval Research Logistics, Vol. 43, pp. 765-795, 1996.
    • (1996) Naval Research Logistics , vol.43 , pp. 765-795
    • Benson, H.P.1
  • 13
    • 0001822918 scopus 로고
    • A global optimization algorithm for linear fractional and bilinear programs
    • QUESADA, I., and GROSSMANN, I., A Global Optimization Algorithm for Linear Fractional and Bilinear Programs, Journal of Global Optimization, Vol. 6, pp. 39-76, 1995.
    • (1995) Journal of Global Optimization , vol.6 , pp. 39-76
    • Quesada, I.1    Grossmann, I.2
  • 14
    • 0006805980 scopus 로고    scopus 로고
    • Minimizing sums and products of linear fractional functions over a polytope
    • KONNO, H., and YAMASHITA, H., Minimizing Sums and Products of Linear Fractional Functions over a Polytope, Naval Research Logistics, Vol. 46, pp. 583-596, 1999.
    • (1999) Naval Research Logistics , vol.46 , pp. 583-596
    • Konno, H.1    Yamashita, H.2
  • 15
    • 0006761358 scopus 로고    scopus 로고
    • Minimization of the sum of three linear fractional functions
    • KONNO, H., and ABE, N., Minimization of the Sum of Three Linear Fractional Functions, Journal of Global Optimization, Vol. 15, pp. 419-432, 1999.
    • (1999) Journal of Global Optimization , vol.15 , pp. 419-432
    • Konno, H.1    Abe, N.2
  • 16
    • 0006805979 scopus 로고    scopus 로고
    • A branch-and-bound algorithm for solving low-rank linear multiplicative and fractional programming problems
    • KONNO, H., and FUKAISHI, K., A Branch-and-Bound Algorithm for Solving Low-Rank Linear Multiplicative and Fractional Programming Problems, Journal of Global Optimization, Vol. 18, pp. 283-299, 2000.
    • (2000) Journal of Global Optimization , vol.18 , pp. 283-299
    • Konno, H.1    Fukaishi, K.2
  • 17
    • 0001327501 scopus 로고
    • αBB: A global optimization method for general constrained nonconvex problems
    • ANDROULAKIS, I. P., MARANAS, C. D., and FLOUDAS, C. A., αBB: A Global Optimization Method for General Constrained Nonconvex Problems, Journal of Global Optimization, Vol. 7, pp. 337-363, 1995.
    • (1995) Journal of Global Optimization , vol.7 , pp. 337-363
    • Androulakis, I.P.1    Maranas, C.D.2    Floudas, C.A.3
  • 18
    • 31244435953 scopus 로고    scopus 로고
    • A branch-and-bound algorithm for maximizing the sum of several linear ratios
    • KUNO, T., A Branch-and-Bound Algorithm for Maximizing the Sum of Several Linear Ratios, Journal of Global Optimization, Vol. 22, pp. 155-174, 2002.
    • (2002) Journal of Global Optimization , vol.22 , pp. 155-174
    • Kuno, T.1
  • 21
    • 0000873824 scopus 로고
    • Fractional programming
    • Edited by R. Horst and P. M. Pardalos, Kluwer Academic Publishers, Dordrecht, Netherlands
    • SCHAIBLE, S., Fractional Programming, Handbook of Global Optimization, Edited by R. Horst and P. M. Pardalos, Kluwer Academic Publishers, Dordrecht, Netherlands, 1995.
    • (1995) Handbook of Global Optimization
    • Schaible, S.1
  • 22
    • 0344664089 scopus 로고    scopus 로고
    • Generating sum-of-ratios test problems in global optimization
    • BENSON, H. P., Generating Sum-of-Ratios Test Problems in Global Optimization, Journal of Optimization Theory and Applications, Vol. 119, pp. 615-621, 2003.
    • (2003) Journal of Optimization Theory and Applications , vol.119 , pp. 615-621
    • Benson, H.P.1
  • 23
    • 0000261286 scopus 로고
    • Programming with linear fractional functionals
    • CHARNES, A., and COOPER, W. W., Programming with Linear Fractional Functionals, Naval Research Logistics Quarterly, Vol. 19, pp. 181-186, 1962.
    • (1962) Naval Research Logistics Quarterly , vol.19 , pp. 181-186
    • Charnes, A.1    Cooper, W.W.2
  • 24
    • 0030556719 scopus 로고    scopus 로고
    • Decomposition approach for the global minimization of biconcave functions over polytopes
    • HORST, R., and THOAI, N. V., Decomposition Approach for the Global Minimization of Biconcave Functions over Polytopes, Journal of Optimization Theory and Applications, Vol. 88, pp. 561-583, 1996.
    • (1996) Journal of Optimization Theory and Applications , vol.88 , pp. 561-583
    • Horst, R.1    Thoai, N.V.2
  • 27
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton, New Jersey
    • ROCKAFELLAR, R. T., Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 29
    • 34250387491 scopus 로고
    • An algorithm for nonconvex programming problems
    • HORST, R., An Algorithm for Nonconvex Programming Problems, Mathematical Programming, Vol. 10, pp. 312-321, 1976.
    • (1976) Mathematical Programming , vol.10 , pp. 312-321
    • Horst, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.