메뉴 건너뛰기




Volumn 22, Issue 1-4, 2002, Pages 343-364

Using concave envelopes to globally solve the nonlinear sum of ratios problem

Author keywords

Concave envelope; Fractional functions; Global optimization; Sum of ratios problem

Indexed keywords

GLOBAL OPTIMIZATION;

EID: 84938594373     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1023/a:1013869015288     Document Type: Article
Times cited : (71)

References (30)
  • 2
    • 0030242902 scopus 로고    scopus 로고
    • Deterministic algorithms for constrained concave minimization: A unified critical survey
    • Benson, H.P. (1996), Deterministic algorithms for constrained concave minimization: a unified critical survey, Naval Research Logistics43: 765–795
    • (1996) Naval Research Logistics , vol.43 , pp. 765-795
    • Benson, H.P.1
  • 4
    • 0000003266 scopus 로고    scopus 로고
    • An outcome space branch and bound outer-approximation algorithm for convex multiplicative programming
    • Benson, H.P. (1999), An outcome space branch and bound outer-approximation algorithm for convex multiplicative programming, Journal of Global Optimization15: 315–342
    • (1999) Journal of Global Optimization , vol.15 , pp. 315-342
    • Benson, H.P.1
  • 5
    • 0025522785 scopus 로고
    • Separable concave minimization via partial outer approximation and branch and bound
    • Benson, H.P. (1990), Separable concave minimization via partial outer approximation and branch and bound, Operations Reserch Letters9: 389–394
    • (1990) Operations Reserch Letters , vol.9 , pp. 389-394
    • Benson, H.P.1
  • 9
    • 0003136739 scopus 로고
    • Image space analysis of generalized fractional programs
    • Falk, J.E. and Palocsay, S.W. (1994), Image space analysis of generalized fractional programs, Journal of Global Optimization4: 63–88
    • (1994) Journal of Global Optimization , vol.4 , pp. 63-88
    • Falk, J.E.1    Palocsay, S.W.2
  • 10
    • 0042497912 scopus 로고
    • Boyd and Fraser Publishing Company, Danvers, MA
    • Fourer, R., Gay, D.M. and Kernighan, B.W. (1993), AMPL, a Modeling Language for Mathematical Programming, Boyd and Fraser Publishing Company, Danvers, MA
    • (1993) AMPL
    • Fourer, R.1    Gay, D.M.2    Kernighan, B.W.3
  • 11
    • 0006866699 scopus 로고    scopus 로고
    • Solving the sum-of-ratios problem by an interior point method
    • Freund, R. and Jarre, F. (2001), Solving the sum-of-ratios problem by an interior point method, Journal of Global Optimization19: 83–102
    • (2001) Journal of Global Optimization , vol.19 , pp. 83-102
    • Freund, R.1    Jarre, F.2
  • 12
    • 0043265477 scopus 로고
    • Bilinear programming: An exact algorithm
    • Gallo, G. and Ulkucu, A. (1977), Bilinear programming: an exact algorithm, Mathematical Programming12: 173–194
    • (1977) Mathematical Programming , vol.12 , pp. 173-194
    • Gallo, G.1    Ulkucu, A.2
  • 14
  • 15
    • 0141868669 scopus 로고
    • An algorithm for global minimization of linearly constrained concave quadratic functions
    • Kalantari, B. and Rosen, J.B. (1987), An algorithm for global minimization of linearly constrained concave quadratic functions, Mathematics of Operations Research12: 544–561
    • (1987) Mathematics of Operations Research , vol.12 , pp. 544-561
    • Kalantari, B.1    Rosen, J.B.2
  • 16
    • 0006761358 scopus 로고    scopus 로고
    • Minimization of the sum of three linear fractional functions
    • Konno, H. and Abe, N. (1999), Minimization of the sum of three linear fractional functions, Journal of Global Optimization15: 419–432
    • (1999) Journal of Global Optimization , vol.15 , pp. 419-432
    • Konno, H.1    Abe, N.2
  • 17
    • 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. (2000), A branch and bound algorithm for solving low rank linear multiplicative and fractional programming problems, Journal of Global Optimization18: 283–299
    • (2000) Journal of Global Optimization , vol.18 , pp. 283-299
    • Konno, H.1    Fukaishi, K.2
  • 19
    • 0006796190 scopus 로고
    • Global minimization of a generalized convex multiplicative function
    • Konno, H., Kuno, T. and Yajima, Y. (1994), Global minimization of a generalized convex multiplicative function, Journal of Global Optimization4: 47–62
    • (1994) Journal of Global Optimization , vol.4 , pp. 47-62
    • Konno, H.1    Kuno, T.2    Yajima, Y.3
  • 20
    • 0001404993 scopus 로고    scopus 로고
    • Bond portfolio optimization problems and their application to index tracking: A partial optimization approach
    • Konno, H. and Watanabe, H. (1996), Bond portfolio optimization problems and their application to index tracking: a partial optimization approach, Journal of the Operations Research Society of Japan39: 295–306
    • (1996) Journal of the Operations Research Society of Japan , vol.39 , pp. 295-306
    • Konno, H.1    Watanabe, H.2
  • 21
    • 0002398911 scopus 로고
    • Parametric simplex algorithms for solving a special class of nonconvex minimization problems
    • Konno, H., Yajima, Y. and Matsui, T. (1991), Parametric simplex algorithms for solving a special class of nonconvex minimization problems, Journal of Global Optimization1: 65–81
    • (1991) Journal of Global Optimization , vol.1 , pp. 65-81
    • Konno, H.1    Yajima, Y.2    Matsui, T.3
  • 22
    • 0006805980 scopus 로고    scopus 로고
    • Minimizing sums and products of linear fractional functions over a polytope
    • Konno, H. and Yamashita, H. (1999), Minimizing sums and products of linear fractional functions over a polytope, Naval Research Logistics46: 583–596
    • (1999) Naval Research Logistics , vol.46 , pp. 583-596
    • Konno, H.1    Yamashita, H.2
  • 24
    • 0003446306 scopus 로고    scopus 로고
    • Stanford University, Technical Report SOL 83-20R, Stanford, CA
    • Murtagh, B.A. and Saunders, M.A. (1998), MINOS 5.5 User’s Guide, Stanford University, Technical Report SOL 83-20R, Stanford, CA
    • (1998) MINOS 5.5 User’s Guide
    • Murtagh, B.A.1    Saunders, M.A.2
  • 25
    • 0001822918 scopus 로고
    • A global optimization algorithm for linear fractional and bilinear programs
    • Quesada, I. and Grossman, I. (1995), A global optimization algorithm for linear fractional and bilinear programs, Journal of Global Optimization6: 39–76
    • (1995) Journal of Global Optimization , vol.6 , pp. 39-76
    • Quesada, I.1    Grossman, I.2
  • 26
    • 0022677990 scopus 로고
    • Global minimization of large-scale constrained concave quadratic problems by separable programming
    • Rosen, J.B. and Pardalos, P.M. (1986), Global minimization of large-scale constrained concave quadratic problems by separable programming, Mathematical Programming34: 163–174
    • (1986) Mathematical Programming , vol.34 , pp. 163-174
    • Rosen, J.B.1    Pardalos, P.M.2
  • 27
    • 0000873824 scopus 로고
    • Fractional programming
    • R. Horst and P.M. Pardalos, Kluwer Academic Publishers, Dordrecht, The Netherlands
    • Schaible, S. (1995), Fractional programming, in: R. Horst and P.M. Pardalos (eds), Handbook of Global Optimization, Kluwer Academic Publishers, Dordrecht, The Netherlands, 495–608
    • (1995) Handbook of Global Optimization , pp. 495-608
    • Schaible, S.1
  • 29
    • 0000042501 scopus 로고
    • A note on the sum of a linear and linear-fractional function
    • Schaible, S. (1977), A note on the sum of a linear and linear-fractional function, Naval Research Logistics Quarterly24: 691–693
    • (1977) Naval Research Logistics Quarterly , vol.24 , pp. 691-693
    • Schaible, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.