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Minimizing the weighted number of tardy jobs on multiple machines: A review
Differential optimization in finite-dimensional spaces
1. | School of Information Technology, Jiangxi University of Finance and Economics, Nanchang 330013, China |
2. | School of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, China |
3. | Department of Mathematics, Guangxi University for Nationalities, Nanning 530006, China |
References:
[1] |
F. Archetti and F. Schen, A survey on the global optimization problem: General theory and computational approaches,, Annals of Operations Research, 1 (1984), 87.
doi: 10.1007/BF01876141. |
[2] |
W. Behrman, An Efficient Gradient Flow Method for Unconstrained Optimization,, PhD thesis, (1998).
|
[3] |
J. F. Bonnans and A. Shapiro, Perturbation Analyisis of Optimization Problems,, Springer-Verlag New York Inc., (2000).
doi: 10.1007/978-1-4612-1394-9. |
[4] |
T. D. Chuong, N. Q. Huy and J. C. Yao, Stability of semi-infinite vector optimization problems under functional perturbations,, Journal of Global Optimization, 45 (2009), 583.
doi: 10.1007/s10898-008-9391-x. |
[5] |
W. R. Esposito and C. A. Floudas, Deterministic global optimization in nonlinear optimal control problems,, Journal of Global Optimization, 17 (2000), 97.
doi: 10.1023/A:1026578104213. |
[6] |
Z. G. Feng and K. F. C. Yiu, Manifold relaxations for integer programming,, Journal of Industrial and Managemnt Optimization, 10 (2014), 557.
doi: 10.3934/jimo.2014.10.557. |
[7] |
Y. R. He, Stable pseudomonotone variational inequality in reflexive Banach spaces,, Journal of Mathematical Analysis and Applications, 330 (2007), 352.
doi: 10.1016/j.jmaa.2006.07.063. |
[8] |
X. Q. Hua and N. Yamashita, An inexact coordinate descent method for the weighted $l_1$-regularized convex optimization problem,, Pacific Journal of Optimization, 9 (2013), 567.
|
[9] |
N. Q. Huy and J. C. Yao, Semi-infinite optimization under convex function perturbations: Lipschitz stability,, Journal of Optimization Theory and Application, 148 (2011), 237.
doi: 10.1007/s10957-010-9753-7. |
[10] |
P. Q. Khanh, L. J. Lin and V. S. T. Long, On topological existence theorems and applications to optimization-related problems,, Mathematical Method of Operations Research, 79 (2014), 253.
doi: 10.1007/s00186-014-0462-0. |
[11] |
G. M. Lee and K. B. Lee, Vector variational inequalities for nondifferentiable convex vector optimization problems,, Journal of Global Optimization, 32 (2005), 597.
doi: 10.1007/s10898-004-2696-5. |
[12] |
C. Y. Liu, Z. H. Gong and E. M. Feng, Optimal control for a nonlinear time-delay system in fed-batch fermentation,, Pacific Journal of Optimization, 9 (2013), 595.
|
[13] |
J. Z. Liu, K. F. C. Yiu and K. L. Teo, Optimal investment-consumption problem with constraint,, Journal of Industrial and Management Optimization, 9 (2013), 743.
doi: 10.3934/jimo.2013.9.743. |
[14] |
J. Z. Liu and K. F. C. Yiu, Optimal stochastic differential games with var constraints,, Discrete and Continuous Dynamical Systems, 18 (2013), 1889.
doi: 10.3934/dcdsb.2013.18.1889. |
[15] |
Y. F. Liu, F. L. Wu and K. L. Teo, Conceptual study on applying optimal control theory for generator bidding in power markets,, Automation of Electric Power Systems, 29 (2005), 1. Google Scholar |
[16] |
A. Nagurney, J. Pan and L. Zhao, Human migration networks,, European Journal of Operational Research, 59 (1992), 262.
doi: 10.1016/0377-2217(92)90140-5. |
[17] |
J. S. Pang and D. E. Stewart, Differential variational inequalities,, Mathematical Programming Series A, 113 (2008), 345.
doi: 10.1007/s10107-006-0052-x. |
[18] |
I. Papamichail and C. S. Adjiman, A rigorous global optimization algorithm for problems with ordinary differential equations,, Journal of Global Optimization, 24 (2002), 1.
doi: 10.1023/A:1016259507911. |
[19] |
D. Preda and J. Noailles, Mixed integer programming for a special logic constrained optimal control problem,, Mathematical Programming, 103 (2005), 309.
doi: 10.1007/s10107-005-0584-5. |
[20] |
A. U. Raghunathan, J. R. Pérez-Correa, E. Agosin and L. T. Biegler, Parameter estimation in metabolic flux balance models for batch fermentation-formulation and solution using differential variational inequalities,, Annals of Operations Research, 148 (2006), 251.
doi: 10.1007/s10479-006-0086-8. |
[21] |
S. Sager, H. G. Bock and G. Reinelt, Direct methods with maximal lower bound for mixed-integer optimal control problems,, Mathematical Programming, 118 (2009), 109.
doi: 10.1007/s10107-007-0185-6. |
[22] |
A. B. Singer and P. I. Barton, Global optimization with nonlinear ordinary differential equations,, Journal of Global Optimization, 34 (2006), 159.
doi: 10.1007/s10898-005-7074-4. |
[23] |
A. B. Singer and P. I. Barton, Global solution of linear dynamic embedded optimization problems,, Journal of Optimization Theory and Applications, 121 (2004), 613.
doi: 10.1023/B:JOTA.0000037606.79050.a7. |
[24] |
S. Wang, X. Q. Yang and K. L. Teo, A unified gradient flow approach to constrained nonlinear optimization problems,, Computational Optimization and Applications, 25 (2003), 251.
doi: 10.1023/A:1022973608903. |
[25] |
L. Yang, Y. P. Chen and X. J. Tong, A note on local sensitivity analysis for parametric optimization problem,, Pacific Journal of Optimization, 8 (2012), 185.
|
[26] |
K. F. C. Yiu, W. Y. Yan, K. L. Teo and S. Y. Low, A new hybrid descent method with application to the optimal design of finite precision FIR filters,, Optimization Methods and Software, 25 (2010), 725.
doi: 10.1080/10556780903254104. |
[27] |
J. Zeng, S. J. Li, W. Y. Zhang and X. W. Xue, Stability results for convex vector-valued optimization problems,, Positivity, 15 (2011), 441.
doi: 10.1007/s11117-010-0093-5. |
[28] |
X. G. Zhou and B. Y. Cao, New global optimality conditions for cubic minimization subject to box or bivalent constraint,, Pacific Journal of Optimization, 8 (2012), 631.
|
[29] |
L. Zhu and F. Q. Xia, Scalarization method for Levitin-Polyak well-posedness of vectorial optimization problems,, Mathematical Method of Operations Research, 76 (2012), 361.
doi: 10.1007/s00186-012-0410-9. |
show all references
References:
[1] |
F. Archetti and F. Schen, A survey on the global optimization problem: General theory and computational approaches,, Annals of Operations Research, 1 (1984), 87.
doi: 10.1007/BF01876141. |
[2] |
W. Behrman, An Efficient Gradient Flow Method for Unconstrained Optimization,, PhD thesis, (1998).
|
[3] |
J. F. Bonnans and A. Shapiro, Perturbation Analyisis of Optimization Problems,, Springer-Verlag New York Inc., (2000).
doi: 10.1007/978-1-4612-1394-9. |
[4] |
T. D. Chuong, N. Q. Huy and J. C. Yao, Stability of semi-infinite vector optimization problems under functional perturbations,, Journal of Global Optimization, 45 (2009), 583.
doi: 10.1007/s10898-008-9391-x. |
[5] |
W. R. Esposito and C. A. Floudas, Deterministic global optimization in nonlinear optimal control problems,, Journal of Global Optimization, 17 (2000), 97.
doi: 10.1023/A:1026578104213. |
[6] |
Z. G. Feng and K. F. C. Yiu, Manifold relaxations for integer programming,, Journal of Industrial and Managemnt Optimization, 10 (2014), 557.
doi: 10.3934/jimo.2014.10.557. |
[7] |
Y. R. He, Stable pseudomonotone variational inequality in reflexive Banach spaces,, Journal of Mathematical Analysis and Applications, 330 (2007), 352.
doi: 10.1016/j.jmaa.2006.07.063. |
[8] |
X. Q. Hua and N. Yamashita, An inexact coordinate descent method for the weighted $l_1$-regularized convex optimization problem,, Pacific Journal of Optimization, 9 (2013), 567.
|
[9] |
N. Q. Huy and J. C. Yao, Semi-infinite optimization under convex function perturbations: Lipschitz stability,, Journal of Optimization Theory and Application, 148 (2011), 237.
doi: 10.1007/s10957-010-9753-7. |
[10] |
P. Q. Khanh, L. J. Lin and V. S. T. Long, On topological existence theorems and applications to optimization-related problems,, Mathematical Method of Operations Research, 79 (2014), 253.
doi: 10.1007/s00186-014-0462-0. |
[11] |
G. M. Lee and K. B. Lee, Vector variational inequalities for nondifferentiable convex vector optimization problems,, Journal of Global Optimization, 32 (2005), 597.
doi: 10.1007/s10898-004-2696-5. |
[12] |
C. Y. Liu, Z. H. Gong and E. M. Feng, Optimal control for a nonlinear time-delay system in fed-batch fermentation,, Pacific Journal of Optimization, 9 (2013), 595.
|
[13] |
J. Z. Liu, K. F. C. Yiu and K. L. Teo, Optimal investment-consumption problem with constraint,, Journal of Industrial and Management Optimization, 9 (2013), 743.
doi: 10.3934/jimo.2013.9.743. |
[14] |
J. Z. Liu and K. F. C. Yiu, Optimal stochastic differential games with var constraints,, Discrete and Continuous Dynamical Systems, 18 (2013), 1889.
doi: 10.3934/dcdsb.2013.18.1889. |
[15] |
Y. F. Liu, F. L. Wu and K. L. Teo, Conceptual study on applying optimal control theory for generator bidding in power markets,, Automation of Electric Power Systems, 29 (2005), 1. Google Scholar |
[16] |
A. Nagurney, J. Pan and L. Zhao, Human migration networks,, European Journal of Operational Research, 59 (1992), 262.
doi: 10.1016/0377-2217(92)90140-5. |
[17] |
J. S. Pang and D. E. Stewart, Differential variational inequalities,, Mathematical Programming Series A, 113 (2008), 345.
doi: 10.1007/s10107-006-0052-x. |
[18] |
I. Papamichail and C. S. Adjiman, A rigorous global optimization algorithm for problems with ordinary differential equations,, Journal of Global Optimization, 24 (2002), 1.
doi: 10.1023/A:1016259507911. |
[19] |
D. Preda and J. Noailles, Mixed integer programming for a special logic constrained optimal control problem,, Mathematical Programming, 103 (2005), 309.
doi: 10.1007/s10107-005-0584-5. |
[20] |
A. U. Raghunathan, J. R. Pérez-Correa, E. Agosin and L. T. Biegler, Parameter estimation in metabolic flux balance models for batch fermentation-formulation and solution using differential variational inequalities,, Annals of Operations Research, 148 (2006), 251.
doi: 10.1007/s10479-006-0086-8. |
[21] |
S. Sager, H. G. Bock and G. Reinelt, Direct methods with maximal lower bound for mixed-integer optimal control problems,, Mathematical Programming, 118 (2009), 109.
doi: 10.1007/s10107-007-0185-6. |
[22] |
A. B. Singer and P. I. Barton, Global optimization with nonlinear ordinary differential equations,, Journal of Global Optimization, 34 (2006), 159.
doi: 10.1007/s10898-005-7074-4. |
[23] |
A. B. Singer and P. I. Barton, Global solution of linear dynamic embedded optimization problems,, Journal of Optimization Theory and Applications, 121 (2004), 613.
doi: 10.1023/B:JOTA.0000037606.79050.a7. |
[24] |
S. Wang, X. Q. Yang and K. L. Teo, A unified gradient flow approach to constrained nonlinear optimization problems,, Computational Optimization and Applications, 25 (2003), 251.
doi: 10.1023/A:1022973608903. |
[25] |
L. Yang, Y. P. Chen and X. J. Tong, A note on local sensitivity analysis for parametric optimization problem,, Pacific Journal of Optimization, 8 (2012), 185.
|
[26] |
K. F. C. Yiu, W. Y. Yan, K. L. Teo and S. Y. Low, A new hybrid descent method with application to the optimal design of finite precision FIR filters,, Optimization Methods and Software, 25 (2010), 725.
doi: 10.1080/10556780903254104. |
[27] |
J. Zeng, S. J. Li, W. Y. Zhang and X. W. Xue, Stability results for convex vector-valued optimization problems,, Positivity, 15 (2011), 441.
doi: 10.1007/s11117-010-0093-5. |
[28] |
X. G. Zhou and B. Y. Cao, New global optimality conditions for cubic minimization subject to box or bivalent constraint,, Pacific Journal of Optimization, 8 (2012), 631.
|
[29] |
L. Zhu and F. Q. Xia, Scalarization method for Levitin-Polyak well-posedness of vectorial optimization problems,, Mathematical Method of Operations Research, 76 (2012), 361.
doi: 10.1007/s00186-012-0410-9. |
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