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Outcome space algorithm for generalized multiplicative problems and optimization over the efficient set
1. | School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, No. 1 Dai Co Viet, Hai Ba Trung, Hanoi, Vietnam, Vietnam |
References:
[1] |
A. M. Ashtiani and P. A. V. Ferreira, On the Solution of Generalized Multiplicative Extremum Problems,, J. Optim. Theory Appl., 149 (2011), 411.
doi: 10.1007/s10957-010-9782-2. |
[2] |
H. P. Benson, A Bisection-Extreme Point Search Algorithm for Optimizing over the Efficient Set in the Linear Dependence Case,, J. Global Optim., 3 (1993), 95.
doi: 10.1007/BF01100242. |
[3] |
H. P. Benson and D. Lee, Outcome-based algorithm for optimizing over the efficient set of a bicriteria linear programming problem,, J. Optim. Theory Appl., 88 (1996), 77.
doi: 10.1007/BF02192023. |
[4] |
H. P. Benson, Global maximization of a generalized concave multiplicative function,, J. Optim. Theory Appl., 137 (2008), 105.
doi: 10.1007/s10957-007-9323-9. |
[5] |
J. Fulop and L. D. Muu, Branch-and-bound variant of an outcome-based algorithm for optimizing over the efficient set of a bicriteria linear programming problem,, J. Optim. Theory Appl., 105 (2000), 37.
doi: 10.1023/A:1004657827134. |
[6] |
R. Horst and N. V. Thoai, Utility Function Programs and Optimization over the Efficient Set in Multiple-Objective Decision Making,, J. Optim. Theory Appl., 92 (1997), 605.
doi: 10.1023/A:1022659523991. |
[7] |
H. Isermann and R. E. Steuer, Computational Experience Concerning Payoff Tables and Minimum Criterion Values over the Efficient Set,, Eur. J. Oper. Res., 33 (1988), 91.
doi: 10.1016/0377-2217(88)90257-3. |
[8] |
B. Jaumard, C. Meyer and H. Tuy, Generalized convex multiplicative programming via quasiconcave minimization,, J. Global Optim., 10 (1997), 229.
doi: 10.1023/A:1008203116882. |
[9] |
N. T. B. Kim, L. T. H. An and T. M. Thanh, Outcome-Space Polyblock Approximation Algorithm for Optimizing over Efficient Sets,, in Modelling, 14 (2008), 234. Google Scholar |
[10] |
N. T. B. Kim and L. D. Muu, On the projection of the efficient set and potential applications,, Optim. 51 (2002), 51 (2002), 401.
doi: 10.1080/02331930290019486. |
[11] |
N. T. B. Kim and T. N. Thang, Optimization over the Efficient Set of a Bicriteria Convex Programming Problem,, Pacific J. Optim., 9 (2013), 103.
|
[12] |
H. Konno, T. Kuno and Y. Yajima, Global Minimization of a Generalized Convex Multiplicative Function,, J. Global Optim, 4 (1994), 47.
doi: 10.1007/BF01096534. |
[13] |
D. T. Luc, Theory of Vector Optimization,, Springer-Verlag, (1989).
|
[14] |
L. T. Luc and L. D. Muu, Global optimization approach to optimizing over the efficient set,, in Recent Advances in Optimization (eds. P. Gritzmann, 452 (1997), 183.
doi: 10.1007/978-3-642-59073-3_13. |
[15] |
D. T. Luc, T. Q. Phong and M. Volle, Scalarizing Functions for Generating the Weakly Efficient Solution Set in Convex Multiobjective Problems,, SIAM J. Optim., 15 (2005), 987.
doi: 10.1137/040603097. |
[16] |
L. D. Muu and B. T. Tam, Minimizing the sum of a convex function and the product of two affine functions over a convex set,, Optim., 24 (1992), 57.
doi: 10.1080/02331939208843779. |
[17] |
H. X. Phu, On efficient sets in $\mathbbR^2$,, Vietnam J. Math., 33 (2005), 463.
|
[18] |
T. N. Thang, Outcome-based branch and bound algorithm for optimization over the efficient set and its application,, in Some Current Advanced Researches on Information and Computer Science in Vietnam, 341 (2015), 31.
doi: 10.1007/978-3-319-14633-1_3. |
[19] |
N. V. Thoai, Conical algorithm in global optimization for optimizing over efficient sets,, J. Global Optim., 18 (2000), 321.
doi: 10.1023/A:1026544116333. |
[20] |
H. Tuy, Convex Analysis and Global Optimization,, Kluwer Academic Publishers, (1998).
doi: 10.1007/978-1-4757-2809-5. |
[21] |
Y. Yamamoto, Optimization over the efficient set: Overview,, J. Global Optim., 22 (2002), 285.
doi: 10.1023/A:1013875600711. |
[22] |
P. L. Yu, Multiple-Criteria Decision Making,, Plenum Press, (1985).
doi: 10.1007/978-1-4684-8395-6. |
show all references
References:
[1] |
A. M. Ashtiani and P. A. V. Ferreira, On the Solution of Generalized Multiplicative Extremum Problems,, J. Optim. Theory Appl., 149 (2011), 411.
doi: 10.1007/s10957-010-9782-2. |
[2] |
H. P. Benson, A Bisection-Extreme Point Search Algorithm for Optimizing over the Efficient Set in the Linear Dependence Case,, J. Global Optim., 3 (1993), 95.
doi: 10.1007/BF01100242. |
[3] |
H. P. Benson and D. Lee, Outcome-based algorithm for optimizing over the efficient set of a bicriteria linear programming problem,, J. Optim. Theory Appl., 88 (1996), 77.
doi: 10.1007/BF02192023. |
[4] |
H. P. Benson, Global maximization of a generalized concave multiplicative function,, J. Optim. Theory Appl., 137 (2008), 105.
doi: 10.1007/s10957-007-9323-9. |
[5] |
J. Fulop and L. D. Muu, Branch-and-bound variant of an outcome-based algorithm for optimizing over the efficient set of a bicriteria linear programming problem,, J. Optim. Theory Appl., 105 (2000), 37.
doi: 10.1023/A:1004657827134. |
[6] |
R. Horst and N. V. Thoai, Utility Function Programs and Optimization over the Efficient Set in Multiple-Objective Decision Making,, J. Optim. Theory Appl., 92 (1997), 605.
doi: 10.1023/A:1022659523991. |
[7] |
H. Isermann and R. E. Steuer, Computational Experience Concerning Payoff Tables and Minimum Criterion Values over the Efficient Set,, Eur. J. Oper. Res., 33 (1988), 91.
doi: 10.1016/0377-2217(88)90257-3. |
[8] |
B. Jaumard, C. Meyer and H. Tuy, Generalized convex multiplicative programming via quasiconcave minimization,, J. Global Optim., 10 (1997), 229.
doi: 10.1023/A:1008203116882. |
[9] |
N. T. B. Kim, L. T. H. An and T. M. Thanh, Outcome-Space Polyblock Approximation Algorithm for Optimizing over Efficient Sets,, in Modelling, 14 (2008), 234. Google Scholar |
[10] |
N. T. B. Kim and L. D. Muu, On the projection of the efficient set and potential applications,, Optim. 51 (2002), 51 (2002), 401.
doi: 10.1080/02331930290019486. |
[11] |
N. T. B. Kim and T. N. Thang, Optimization over the Efficient Set of a Bicriteria Convex Programming Problem,, Pacific J. Optim., 9 (2013), 103.
|
[12] |
H. Konno, T. Kuno and Y. Yajima, Global Minimization of a Generalized Convex Multiplicative Function,, J. Global Optim, 4 (1994), 47.
doi: 10.1007/BF01096534. |
[13] |
D. T. Luc, Theory of Vector Optimization,, Springer-Verlag, (1989).
|
[14] |
L. T. Luc and L. D. Muu, Global optimization approach to optimizing over the efficient set,, in Recent Advances in Optimization (eds. P. Gritzmann, 452 (1997), 183.
doi: 10.1007/978-3-642-59073-3_13. |
[15] |
D. T. Luc, T. Q. Phong and M. Volle, Scalarizing Functions for Generating the Weakly Efficient Solution Set in Convex Multiobjective Problems,, SIAM J. Optim., 15 (2005), 987.
doi: 10.1137/040603097. |
[16] |
L. D. Muu and B. T. Tam, Minimizing the sum of a convex function and the product of two affine functions over a convex set,, Optim., 24 (1992), 57.
doi: 10.1080/02331939208843779. |
[17] |
H. X. Phu, On efficient sets in $\mathbbR^2$,, Vietnam J. Math., 33 (2005), 463.
|
[18] |
T. N. Thang, Outcome-based branch and bound algorithm for optimization over the efficient set and its application,, in Some Current Advanced Researches on Information and Computer Science in Vietnam, 341 (2015), 31.
doi: 10.1007/978-3-319-14633-1_3. |
[19] |
N. V. Thoai, Conical algorithm in global optimization for optimizing over efficient sets,, J. Global Optim., 18 (2000), 321.
doi: 10.1023/A:1026544116333. |
[20] |
H. Tuy, Convex Analysis and Global Optimization,, Kluwer Academic Publishers, (1998).
doi: 10.1007/978-1-4757-2809-5. |
[21] |
Y. Yamamoto, Optimization over the efficient set: Overview,, J. Global Optim., 22 (2002), 285.
doi: 10.1023/A:1013875600711. |
[22] |
P. L. Yu, Multiple-Criteria Decision Making,, Plenum Press, (1985).
doi: 10.1007/978-1-4684-8395-6. |
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