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A modified Fletcher-Reeves-Type derivative-free method for symmetric nonlinear equations
Celis-Dennis-Tapia based approach to quadratic fractional programming problems with two quadratic constraints
1. | Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-Ku, Kyoto 606-8501, Japan |
2. | Department of Applied Mathematics and Physics,, Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-Ku, Kyoto 606-8501, Japan |
References:
[1] |
A. Beck, A. Ben-Tal and M. Teboulle, Finding a global optimal solution for a quadratically constrained fractional quadratic problem with applications to the regularized total least squares, SIAM Journal on Matrix Analysis and Applications, 28 (2006), 425-445.
doi: 10.1137/040616851. |
[2] |
A. Beck and Y. C. Eldar, Strong duality in nonconvex quadratic optimization with two quadratic constraints, SIAM Journal on Optimization, 17 (2006), 844-860.
doi: 10.1137/050644471. |
[3] |
H. P. Benson, Fractional programming with convex quadratic forms and functions, European Journal of Operational Research, 173 (2006), 351-369.
doi: 10.1016/j.ejor.2005.02.069. |
[4] |
G. R. Bitran and T. L. Magnanti, Duality and sensitivity analysis for fractional programs, Operations Research, 24 (1976), 675-699.
doi: 10.1287/opre.24.4.675. |
[5] |
M. R. Celis, J. E. Dennis and R. A. Tapia, A trust region strategy for nonlinear equality constrained optimization, in "Numerical Optimization" (eds. P. T. Boggs, R. H. Byrd, R. B. Schnabel), SIAM, Philadelphia, (1985), 71-82. |
[6] |
A. Charnes and W. W. Cooper, Programming with linear fractional functionals, Naval Research Logistics Quarterly, 9 (1962), 181-186.
doi: 10.1002/nav.3800090303. |
[7] |
X. Chen and Y. Yuan, On local solutions of the Celis-Dennis-Tapia subproblem, SIAM Journal on Optimization, 10 (2000), 359-383.
doi: 10.1137/S1052623498335018. |
[8] |
X. Chen and Y. Yuan, On maxima of dual function of the CDT subproblem, Journal of Computational Mathematics, 19 (2001), 113-124. |
[9] |
X. Chen and Y. Yuan, Optimality conditions for CDT subproblem, in "Numerical Linear Algebra and Optimization" (eds. Y. Yuan), Science Press, Beijing, New York, (1999), 111-121. |
[10] |
A. R. Conn, N. I. M. Gould and Ph. L. Toint, "Trust-Region Methods," SIAM, Philadelphia, 2000.
doi: 10.1137/1.9780898719857. |
[11] |
J. P. Crouzeix and J. A. Ferland, Algorithms for generalized fractional programming, Mathematical Programming, 52 (1991), 191-207.
doi: 10.1007/BF01582887. |
[12] |
W. Dinkelbach, On nonlinear fractional programming, Management Science, 13 (1967), 492-498.
doi: 10.1287/mnsc.13.7.492. |
[13] |
J. Gotoh and H. Konno, Maximization of the ratio of two convex quadratic functions over a polytope, Computational Optimization and Applications, 20 (2001), 43-60.
doi: 10.1023/A:1011219422283. |
[14] |
T. Ibaraki, Parametric approaches to fractional programs, Mathematical Programming, 26 (1983), 345-362.
doi: 10.1007/BF02591871. |
[15] |
T. Ibaraki, H. Ishii, J. Iwase, T. Hasegawa and H. Mine, Algorithms for quadratic fractional programming problems, Journal of Operational Research Society of Japan, 19 (1976), 174-191. |
[16] |
R. Jagannathan, On some properties of programming problems in parametric form pertaining to fractional programming, Management Science, 12 (1966), 609-615.
doi: 10.1287/mnsc.12.7.609. |
[17] |
G. Li and Y. Yuan, Compute a Celis-Dennis-Tapia step, Journal of Computational Mathematics, 23 (2005), 463-478. |
[18] |
J. Peng and Y. Yuan, Optimality conditions for the minimization of a quadratic with two quadratic constraints, SIAM Journal on Optimization, 7 (1997), 579-594.
doi: 10.1137/S1052623494261520. |
[19] |
M. J. D. Powell and Y. Yuan, A trust region algorithm for equality constrained optimization, Mathematical Programming, 49 (1991), 189-211.
doi: 10.1007/BF01588787. |
[20] |
J. Von Neumann, Über ein es Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpuntsatzes, in "Ergebnisse eines mathematicschen Kolloquiums (8)" (eds. K. Menger), Leipzig und Wien, (1937), 73-83. |
[21] |
Y. Ye and S. Zhang, New results on quadratic minimization, SIAM Journal on Optimization, 14 (2003), 245-267.
doi: 10.1137/S105262340139001X. |
[22] |
Y. Yuan, On a subproblem of trust region algorithms for constrained optimization, Mathematical Programming, 47 (1990), 53-63.
doi: 10.1007/BF01580852. |
[23] |
Y. Yuan, A dual algorithm for minimizing a quadratic function with two quadratic constraints, Journal of Computational Mathematics, 9 (1991), 348-359. |
[24] |
Y. Zhang, Computing a Celis-Dennis-Tapia trust-region step for equality constrained optimization, Mathematical Programming, 55 (1992), 109-124.
doi: 10.1007/BF01581194. |
show all references
References:
[1] |
A. Beck, A. Ben-Tal and M. Teboulle, Finding a global optimal solution for a quadratically constrained fractional quadratic problem with applications to the regularized total least squares, SIAM Journal on Matrix Analysis and Applications, 28 (2006), 425-445.
doi: 10.1137/040616851. |
[2] |
A. Beck and Y. C. Eldar, Strong duality in nonconvex quadratic optimization with two quadratic constraints, SIAM Journal on Optimization, 17 (2006), 844-860.
doi: 10.1137/050644471. |
[3] |
H. P. Benson, Fractional programming with convex quadratic forms and functions, European Journal of Operational Research, 173 (2006), 351-369.
doi: 10.1016/j.ejor.2005.02.069. |
[4] |
G. R. Bitran and T. L. Magnanti, Duality and sensitivity analysis for fractional programs, Operations Research, 24 (1976), 675-699.
doi: 10.1287/opre.24.4.675. |
[5] |
M. R. Celis, J. E. Dennis and R. A. Tapia, A trust region strategy for nonlinear equality constrained optimization, in "Numerical Optimization" (eds. P. T. Boggs, R. H. Byrd, R. B. Schnabel), SIAM, Philadelphia, (1985), 71-82. |
[6] |
A. Charnes and W. W. Cooper, Programming with linear fractional functionals, Naval Research Logistics Quarterly, 9 (1962), 181-186.
doi: 10.1002/nav.3800090303. |
[7] |
X. Chen and Y. Yuan, On local solutions of the Celis-Dennis-Tapia subproblem, SIAM Journal on Optimization, 10 (2000), 359-383.
doi: 10.1137/S1052623498335018. |
[8] |
X. Chen and Y. Yuan, On maxima of dual function of the CDT subproblem, Journal of Computational Mathematics, 19 (2001), 113-124. |
[9] |
X. Chen and Y. Yuan, Optimality conditions for CDT subproblem, in "Numerical Linear Algebra and Optimization" (eds. Y. Yuan), Science Press, Beijing, New York, (1999), 111-121. |
[10] |
A. R. Conn, N. I. M. Gould and Ph. L. Toint, "Trust-Region Methods," SIAM, Philadelphia, 2000.
doi: 10.1137/1.9780898719857. |
[11] |
J. P. Crouzeix and J. A. Ferland, Algorithms for generalized fractional programming, Mathematical Programming, 52 (1991), 191-207.
doi: 10.1007/BF01582887. |
[12] |
W. Dinkelbach, On nonlinear fractional programming, Management Science, 13 (1967), 492-498.
doi: 10.1287/mnsc.13.7.492. |
[13] |
J. Gotoh and H. Konno, Maximization of the ratio of two convex quadratic functions over a polytope, Computational Optimization and Applications, 20 (2001), 43-60.
doi: 10.1023/A:1011219422283. |
[14] |
T. Ibaraki, Parametric approaches to fractional programs, Mathematical Programming, 26 (1983), 345-362.
doi: 10.1007/BF02591871. |
[15] |
T. Ibaraki, H. Ishii, J. Iwase, T. Hasegawa and H. Mine, Algorithms for quadratic fractional programming problems, Journal of Operational Research Society of Japan, 19 (1976), 174-191. |
[16] |
R. Jagannathan, On some properties of programming problems in parametric form pertaining to fractional programming, Management Science, 12 (1966), 609-615.
doi: 10.1287/mnsc.12.7.609. |
[17] |
G. Li and Y. Yuan, Compute a Celis-Dennis-Tapia step, Journal of Computational Mathematics, 23 (2005), 463-478. |
[18] |
J. Peng and Y. Yuan, Optimality conditions for the minimization of a quadratic with two quadratic constraints, SIAM Journal on Optimization, 7 (1997), 579-594.
doi: 10.1137/S1052623494261520. |
[19] |
M. J. D. Powell and Y. Yuan, A trust region algorithm for equality constrained optimization, Mathematical Programming, 49 (1991), 189-211.
doi: 10.1007/BF01588787. |
[20] |
J. Von Neumann, Über ein es Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpuntsatzes, in "Ergebnisse eines mathematicschen Kolloquiums (8)" (eds. K. Menger), Leipzig und Wien, (1937), 73-83. |
[21] |
Y. Ye and S. Zhang, New results on quadratic minimization, SIAM Journal on Optimization, 14 (2003), 245-267.
doi: 10.1137/S105262340139001X. |
[22] |
Y. Yuan, On a subproblem of trust region algorithms for constrained optimization, Mathematical Programming, 47 (1990), 53-63.
doi: 10.1007/BF01580852. |
[23] |
Y. Yuan, A dual algorithm for minimizing a quadratic function with two quadratic constraints, Journal of Computational Mathematics, 9 (1991), 348-359. |
[24] |
Y. Zhang, Computing a Celis-Dennis-Tapia trust-region step for equality constrained optimization, Mathematical Programming, 55 (1992), 109-124.
doi: 10.1007/BF01581194. |
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