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Volumn 189, Issue 2, 2007, Pages 1624-1636

An efficient algorithm for globally minimizing sum of quadratic ratios problem with nonconvex quadratic constraints

Author keywords

Branch and bound; Lagrangian relaxation; QSRP

Indexed keywords

ALGORITHMS; BRANCH AND BOUND METHOD; CONSTRAINT THEORY; GLOBAL OPTIMIZATION; LAGRANGE MULTIPLIERS; PROBLEM SOLVING;

EID: 34249077665     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.12.034     Document Type: Article
Times cited : (22)

References (19)
  • 1
    • 0001404993 scopus 로고    scopus 로고
    • Bond protfolio optimization problems and their application to index tracking: a partial optimization approach
    • Konno H., and Inori M. Bond protfolio optimization problems and their application to index tracking: a partial optimization approach. Journal of Operations Research Society of Japan 39 (1996) 295-306
    • (1996) Journal of Operations Research Society of Japan , vol.39 , pp. 295-306
    • Konno, H.1    Inori, M.2
  • 2
    • 0001051560 scopus 로고
    • Conic approximation and collinear scaling for optimizers
    • Davidon W.C. Conic approximation and collinear scaling for optimizers. SIAM Journal of Numerical Analysis 17 (1980) 268-281
    • (1980) SIAM Journal of Numerical Analysis , vol.17 , pp. 268-281
    • Davidon, W.C.1
  • 3
    • 0035729439 scopus 로고    scopus 로고
    • A conic trust-region method for nonlinearly constrained optimization
    • Wenyu S., and Yaxiang Y. A conic trust-region method for nonlinearly constrained optimization. Annals of Operations Research 103 (2001) 175-191
    • (2001) Annals of Operations Research , vol.103 , pp. 175-191
    • Wenyu, S.1    Yaxiang, Y.2
  • 4
    • 0025519753 scopus 로고
    • Deriving collinear scaling algorithms as extensions of quasi-Newton methods and the local convergence of DFP and BFGS related collinear scaling algorithm
    • Ariyawansa K.A. Deriving collinear scaling algorithms as extensions of quasi-Newton methods and the local convergence of DFP and BFGS related collinear scaling algorithm. Mathematical Programming 49 (1990) 23-48
    • (1990) Mathematical Programming , vol.49 , pp. 23-48
    • Ariyawansa, K.A.1
  • 5
    • 0020802854 scopus 로고
    • Parametric approaches to fractional programs
    • Ibaraki T. Parametric approaches to fractional programs. Mathematical Programming 26 (1983) 345-362
    • (1983) Mathematical Programming , vol.26 , pp. 345-362
    • Ibaraki, T.1
  • 6
    • 0037125655 scopus 로고    scopus 로고
    • Fractional programming with absolute-value functions
    • Chadha S.S. Fractional programming with absolute-value functions. European Journal of Operational Research 141 (2002) 233-238
    • (2002) European Journal of Operational Research , vol.141 , pp. 233-238
    • Chadha, S.S.1
  • 7
    • 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 22 (2002) 155-174
    • (2002) Journal of Global Optimization , vol.22 , pp. 155-174
    • Kuno, T.1
  • 8
    • 33646137128 scopus 로고    scopus 로고
    • Global optimization for sum of linear ratios problem with coefficients
    • Shen P.P., and Wang C.F. Global optimization for sum of linear ratios problem with coefficients. Applied Mathematics and Computation 176 (2006) 219-229
    • (2006) Applied Mathematics and Computation , vol.176 , pp. 219-229
    • Shen, P.P.1    Wang, C.F.2
  • 9
    • 84938594373 scopus 로고    scopus 로고
    • Using concave envelopes to globally solve the nonlinear sum of ratios problem
    • Benson H.P. Using concave envelopes to globally solve the nonlinear sum of ratios problem. Journal of Global Optimization 22 (2002) 343-364
    • (2002) Journal of Global Optimization , vol.22 , pp. 343-364
    • Benson, H.P.1
  • 10
    • 9744254460 scopus 로고    scopus 로고
    • Global optimization algorithm for the nonlinear sum of ratios problem
    • Benson H.P. Global optimization algorithm for the nonlinear sum of ratios problem. Journal of Optimization Theory and Application 112 (2002) 1-29
    • (2002) Journal of Optimization Theory and Application , vol.112 , pp. 1-29
    • Benson, H.P.1
  • 11
    • 0006866699 scopus 로고    scopus 로고
    • Solving the sum-of-ratios problem by an interior-point method
    • Freund R.W., and Jarre F. Solving the sum-of-ratios problem by an interior-point method. Journal of Global Optimization 19 (2001) 83-102
    • (2001) Journal of Global Optimization , vol.19 , pp. 83-102
    • Freund, R.W.1    Jarre, F.2
  • 13
    • 0000322706 scopus 로고
    • Implicit application of polynomial filters in a K-step Arnoldi method
    • Sorensen D.C. Implicit application of polynomial filters in a K-step Arnoldi method. SIAM Journal on Matrix Analysis and Applications 13 (1992) 357-385
    • (1992) SIAM Journal on Matrix Analysis and Applications , vol.13 , pp. 357-385
    • Sorensen, D.C.1
  • 14
    • 31244432959 scopus 로고    scopus 로고
    • A global optimization algorithm using lagrangian underestimates and the interval Newton method
    • Voorhis T.V. A global optimization algorithm using lagrangian underestimates and the interval Newton method. Journal of Global Optimization 24 (2002) 349-370
    • (2002) Journal of Global Optimization , vol.24 , pp. 349-370
    • Voorhis, T.V.1
  • 15
    • 0039415676 scopus 로고    scopus 로고
    • Lagrange duality and partitioning techniques in nonconvex global optimization
    • Dur M., and Horst R. Lagrange duality and partitioning techniques in nonconvex global optimization. Journal of Optimization Theory and Applications 95 (1997) 347-369
    • (1997) Journal of Optimization Theory and Applications , vol.95 , pp. 347-369
    • Dur, M.1    Horst, R.2
  • 16
    • 0035479933 scopus 로고    scopus 로고
    • Maximization of the ratio of two convex quadratic functions over a polytope
    • Gotoh J.Y., and Konno H. Maximization of the ratio of two convex quadratic functions over a polytope. Computational Optimization and Applications 20 (2001) 43-60
    • (2001) Computational Optimization and Applications , vol.20 , pp. 43-60
    • Gotoh, J.Y.1    Konno, H.2
  • 17
    • 4244142305 scopus 로고    scopus 로고
    • Rigorous Global Search: Continuous Problems
    • Kluwer Academic Publishers, Dordrecht
    • Kearfott R.B. Rigorous Global Search: Continuous Problems. Nonconvex Optimization and Its Applications vol. 13 (1996), Kluwer Academic Publishers, Dordrecht
    • (1996) Nonconvex Optimization and Its Applications , vol.13
    • Kearfott, R.B.1
  • 18
    • 4043135727 scopus 로고    scopus 로고
    • On the global optimization of sums of linear fractional functions over a convex set
    • Benson H.P. On the global optimization of sums of linear fractional functions over a convex set. Journal of Optimization Theory and Application 121 (2004) 19-39
    • (2004) Journal of Optimization Theory and Application , vol.121 , pp. 19-39
    • Benson, H.P.1
  • 19
    • 0344166134 scopus 로고    scopus 로고
    • A branch and bound method via d.c. optimization algorithms and ellipsoidal technique for box constrained nonconvex quadratic problems
    • An L.T.H., and Tao P.D. A branch and bound method via d.c. optimization algorithms and ellipsoidal technique for box constrained nonconvex quadratic problems. Journal of Global Optimization 13 (1998) 171-206
    • (1998) Journal of Global Optimization , vol.13 , pp. 171-206
    • An, L.T.H.1    Tao, P.D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.