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Doubly nonnegative relaxation method for solving multiple objective quadratic programming problems
1. | Department of Mathematics, Shanghai University, Shanghai 200444, China, China |
References:
[1] |
E. E. Ammar, On solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem,, Inform. Sci., 178 (2008), 468.
doi: 10.1016/j.ins.2007.03.029. |
[2] |
E. E. Ammar, On fuzzy random multiobjective quadratic programming,, European J. Oper. Res., 193 (2009), 329.
doi: 10.1016/j.ejor.2007.11.031. |
[3] |
Y. Q. Bai, and C. H. Guo and L. M. Sun, A new algorithm for solving nonconvex quadratic programming over an ice cream cone,, Pac. J. Optim., 8 (2012), 651.
|
[4] |
A. Berman and N. Shaked-Monderer, Completely Positive Matrices,, World Scientific Publishing Co., (2003).
doi: 10.1142/9789812795212. |
[5] |
H. Bonnel and N. S. Pham, Nonsmooth optimization over the (weakly or properly) Pareto set of a linear-quadratic multi-objective control problem: Explicit optimality conditions,, J. Ind. Manag. Optim., 7 (2011), 789.
doi: 10.3934/jimo.2011.7.789. |
[6] |
I. M. Bomze, Copositive optimization-recent developments and applications,, European J. Oper. Res., 216 (2012), 509.
doi: 10.1016/j.ejor.2011.04.026. |
[7] |
S. Boyd and L. Vandenberghe, Convex Optimization,, Cambridge University Press, (2004).
|
[8] |
S. Burer, On the copositive representation of binary and continuous nonconvex quadratic programs,, Math. Program., 210 (2009), 479.
doi: 10.1007/s10107-008-0223-z. |
[9] |
S. Burer, Optimizing a polyhedral-semidefinite relaxation of completely positive programs,, Math. Program. Comput., 2 (2010), 1.
doi: 10.1007/s12532-010-0010-8. |
[10] |
O. Dandekar, W. Plishker, S. Bhattacharyya and R. Shekhar, Multi-objective optimization for reconfigurable implementation of medical image registration,, International Journal of Reconfigurable Computing, 2008 (2009), 1. Google Scholar |
[11] |
P. H. Diananda, On non-negative forms in real variables some or all of which are non-negative,, Proc. Cambridge Philos. Soc., 58 (1962), 17.
doi: 10.1017/S0305004100036185. |
[12] |
P. Dickinson and L. Gijben, On the Computational Complexity of Membership Problems for the Completely Positive Cone and its Dual,, Technical Report, (2011). Google Scholar |
[13] |
M. Grant and S. Boyd, CVX: Matlab Software for Disciplined Convex Programming,, version 1.21, (2011). Google Scholar |
[14] |
Y. Hu, Efficiency Theory of Multiobjective Programming,, Shanghai Scientific and Technical Publishers, (1994). Google Scholar |
[15] |
P. Korhonen and G. Y. Yu, A reference direction approach to multiple objective quadratic-linear programming,, European Journal of Operational Research, 102 (1997), 601.
doi: 10.1016/S0377-2217(96)00245-7. |
[16] |
C. Lu, S.-C. Fang, Q. W. Jin, Qingwei, Z. B. Wang and W. X. Xing, KKT solution and conic relaxation for solving quadratically constrained quadratic programming problems,, SIAM J. Optim., 21 (2011), 1475.
doi: 10.1137/100793955. |
[17] |
R. T. Marler and J. S. Arora, The weighted sum method for multi-objective optimization: New insights,, Struct. Multidiscip. Optim., 41 (2010), 853.
doi: 10.1007/s00158-009-0460-7. |
[18] |
J. P. Xu and J. Li, A class of stochastic optimization problems with one quadratic & several linear objective functions and extended portfolio selection model,, J. Comput. Appl. Math., 146 (2002), 99.
doi: 10.1016/S0377-0427(02)00421-1. |
[19] |
J. P. Xu and J. Li, Multiple Objective Decision Making Theory and Methods,, Tsinghua University Press, (2005). Google Scholar |
[20] |
B. R. Ye and L. H. Yu, Generating noninferior set of a multi-objective quadratic programming and application,, Water Resources and Power, 9 (1991), 102. Google Scholar |
show all references
References:
[1] |
E. E. Ammar, On solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem,, Inform. Sci., 178 (2008), 468.
doi: 10.1016/j.ins.2007.03.029. |
[2] |
E. E. Ammar, On fuzzy random multiobjective quadratic programming,, European J. Oper. Res., 193 (2009), 329.
doi: 10.1016/j.ejor.2007.11.031. |
[3] |
Y. Q. Bai, and C. H. Guo and L. M. Sun, A new algorithm for solving nonconvex quadratic programming over an ice cream cone,, Pac. J. Optim., 8 (2012), 651.
|
[4] |
A. Berman and N. Shaked-Monderer, Completely Positive Matrices,, World Scientific Publishing Co., (2003).
doi: 10.1142/9789812795212. |
[5] |
H. Bonnel and N. S. Pham, Nonsmooth optimization over the (weakly or properly) Pareto set of a linear-quadratic multi-objective control problem: Explicit optimality conditions,, J. Ind. Manag. Optim., 7 (2011), 789.
doi: 10.3934/jimo.2011.7.789. |
[6] |
I. M. Bomze, Copositive optimization-recent developments and applications,, European J. Oper. Res., 216 (2012), 509.
doi: 10.1016/j.ejor.2011.04.026. |
[7] |
S. Boyd and L. Vandenberghe, Convex Optimization,, Cambridge University Press, (2004).
|
[8] |
S. Burer, On the copositive representation of binary and continuous nonconvex quadratic programs,, Math. Program., 210 (2009), 479.
doi: 10.1007/s10107-008-0223-z. |
[9] |
S. Burer, Optimizing a polyhedral-semidefinite relaxation of completely positive programs,, Math. Program. Comput., 2 (2010), 1.
doi: 10.1007/s12532-010-0010-8. |
[10] |
O. Dandekar, W. Plishker, S. Bhattacharyya and R. Shekhar, Multi-objective optimization for reconfigurable implementation of medical image registration,, International Journal of Reconfigurable Computing, 2008 (2009), 1. Google Scholar |
[11] |
P. H. Diananda, On non-negative forms in real variables some or all of which are non-negative,, Proc. Cambridge Philos. Soc., 58 (1962), 17.
doi: 10.1017/S0305004100036185. |
[12] |
P. Dickinson and L. Gijben, On the Computational Complexity of Membership Problems for the Completely Positive Cone and its Dual,, Technical Report, (2011). Google Scholar |
[13] |
M. Grant and S. Boyd, CVX: Matlab Software for Disciplined Convex Programming,, version 1.21, (2011). Google Scholar |
[14] |
Y. Hu, Efficiency Theory of Multiobjective Programming,, Shanghai Scientific and Technical Publishers, (1994). Google Scholar |
[15] |
P. Korhonen and G. Y. Yu, A reference direction approach to multiple objective quadratic-linear programming,, European Journal of Operational Research, 102 (1997), 601.
doi: 10.1016/S0377-2217(96)00245-7. |
[16] |
C. Lu, S.-C. Fang, Q. W. Jin, Qingwei, Z. B. Wang and W. X. Xing, KKT solution and conic relaxation for solving quadratically constrained quadratic programming problems,, SIAM J. Optim., 21 (2011), 1475.
doi: 10.1137/100793955. |
[17] |
R. T. Marler and J. S. Arora, The weighted sum method for multi-objective optimization: New insights,, Struct. Multidiscip. Optim., 41 (2010), 853.
doi: 10.1007/s00158-009-0460-7. |
[18] |
J. P. Xu and J. Li, A class of stochastic optimization problems with one quadratic & several linear objective functions and extended portfolio selection model,, J. Comput. Appl. Math., 146 (2002), 99.
doi: 10.1016/S0377-0427(02)00421-1. |
[19] |
J. P. Xu and J. Li, Multiple Objective Decision Making Theory and Methods,, Tsinghua University Press, (2005). Google Scholar |
[20] |
B. R. Ye and L. H. Yu, Generating noninferior set of a multi-objective quadratic programming and application,, Water Resources and Power, 9 (1991), 102. Google Scholar |
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