-
Previous Article
Lagrange multiplier rules for approximate solutions in vector optimization
- JIMO Home
- This Issue
-
Next Article
Note on "Cost analysis of the M/M/R machine repair problem with second optional repair: Newton-Quasi method"
A sequential convex program method to DC program with joint chance constraints
1. | School of Mathematical Sciences, Dalian University of Technology, Dalian 116023, China, China |
2. | School of Sciences, Dalian Ocean University, Dalian 116023, China |
3. | School of Computer Science and Technology, Dalian University of Technology, Dalian 116023, China |
References:
[1] |
L. T. H. An, An efficient algorithm for globally minimizing a quadratic function under convex quadratic constraints, Math. Program., 87 (2000), 401-426.
doi: 10.1007/s101070050003. |
[2] |
A. Charnes, W. W. Cooper and H. Symonds, Cost horizons and certainty equivalents: An approach to stochastic programming of heating oil, Manag. Sci., 4 (1958), 235-263. |
[3] |
Y. Gao, "Structured Low Rank Matrix Optimization Problems: A Penalty Approach," Ph.D thesis, National University of Singapore, 2010. |
[4] |
Y. Gao and D. Sun, Calibrating least squares semidefinite programming with equality and inequality constraints, SIAM J. Matrix Anal. Appl., 31 (2009), 1432-1457.
doi: 10.1137/080727075. |
[5] |
M. Grant and S. Boyd, CVX: Matlab software for disciplined convex programming, version 1.21, April, 2011. Available from: http://cvxr.com/cvx. |
[6] |
L. J. Hong, Y. Yang and L. Zhang, Sequential convex approximations to joint chance constrained programs: A Monte Carlo approach, Oper. Res., 59 (2011), 617-630.
doi: 10.1287/opre.1100.0910. |
[7] |
R. Horst and N. V. Thoni, DC programming: Overview, J. Optim. Theory Appl., 103 (1999), 1-43. |
[8] |
D. Klatte and W. Li, Asymptotic constraint qualifications and global error bounds for convex inequalities, Math. Program., 84 (1999), 137-160. |
[9] |
A. Nemirovski and A. Shapiro, Convex approximations of chance constrained programs, SIAM J. Optim., 17 (2006), 969-996.
doi: 10.1137/050622328. |
[10] |
R. T. Rockafellar, "Convex Analysis," Princeton Mathematical Series, No. 28, Princeton University Press, Princeton, NJ, 1970. |
[11] |
R. T. Rockafellar and R. J. B. Wets, "Variational Analysis," Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 317, Springer, New York, 1998. |
[12] |
A. Shapiro, D. Dentcheva and A. Ruszczyński, "Lectures on Stochastic Programming: Modeling and Theory," MPS/SIAM Series on Optimization, 9, SIAM, Philadelphia, PA, 2009. |
show all references
References:
[1] |
L. T. H. An, An efficient algorithm for globally minimizing a quadratic function under convex quadratic constraints, Math. Program., 87 (2000), 401-426.
doi: 10.1007/s101070050003. |
[2] |
A. Charnes, W. W. Cooper and H. Symonds, Cost horizons and certainty equivalents: An approach to stochastic programming of heating oil, Manag. Sci., 4 (1958), 235-263. |
[3] |
Y. Gao, "Structured Low Rank Matrix Optimization Problems: A Penalty Approach," Ph.D thesis, National University of Singapore, 2010. |
[4] |
Y. Gao and D. Sun, Calibrating least squares semidefinite programming with equality and inequality constraints, SIAM J. Matrix Anal. Appl., 31 (2009), 1432-1457.
doi: 10.1137/080727075. |
[5] |
M. Grant and S. Boyd, CVX: Matlab software for disciplined convex programming, version 1.21, April, 2011. Available from: http://cvxr.com/cvx. |
[6] |
L. J. Hong, Y. Yang and L. Zhang, Sequential convex approximations to joint chance constrained programs: A Monte Carlo approach, Oper. Res., 59 (2011), 617-630.
doi: 10.1287/opre.1100.0910. |
[7] |
R. Horst and N. V. Thoni, DC programming: Overview, J. Optim. Theory Appl., 103 (1999), 1-43. |
[8] |
D. Klatte and W. Li, Asymptotic constraint qualifications and global error bounds for convex inequalities, Math. Program., 84 (1999), 137-160. |
[9] |
A. Nemirovski and A. Shapiro, Convex approximations of chance constrained programs, SIAM J. Optim., 17 (2006), 969-996.
doi: 10.1137/050622328. |
[10] |
R. T. Rockafellar, "Convex Analysis," Princeton Mathematical Series, No. 28, Princeton University Press, Princeton, NJ, 1970. |
[11] |
R. T. Rockafellar and R. J. B. Wets, "Variational Analysis," Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 317, Springer, New York, 1998. |
[12] |
A. Shapiro, D. Dentcheva and A. Ruszczyński, "Lectures on Stochastic Programming: Modeling and Theory," MPS/SIAM Series on Optimization, 9, SIAM, Philadelphia, PA, 2009. |
[1] |
Radu Ioan Boţ, Anca Grad, Gert Wanka. Sequential characterization of solutions in convex composite programming and applications to vector optimization. Journal of Industrial and Management Optimization, 2008, 4 (4) : 767-782. doi: 10.3934/jimo.2008.4.767 |
[2] |
Jian Gu, Xiantao Xiao, Liwei Zhang. A subgradient-based convex approximations method for DC programming and its applications. Journal of Industrial and Management Optimization, 2016, 12 (4) : 1349-1366. doi: 10.3934/jimo.2016.12.1349 |
[3] |
Changzhi Wu, Chaojie Li, Qiang Long. A DC programming approach for sensor network localization with uncertainties in anchor positions. Journal of Industrial and Management Optimization, 2014, 10 (3) : 817-826. doi: 10.3934/jimo.2014.10.817 |
[4] |
Jean-François Babadjian, Clément Mifsud, Nicolas Seguin. Relaxation approximation of Friedrichs' systems under convex constraints. Networks and Heterogeneous Media, 2016, 11 (2) : 223-237. doi: 10.3934/nhm.2016.11.223 |
[5] |
Le Thi Hoai An, Tran Duc Quynh, Pham Dinh Tao. A DC programming approach for a class of bilevel programming problems and its application in Portfolio Selection. Numerical Algebra, Control and Optimization, 2012, 2 (1) : 167-185. doi: 10.3934/naco.2012.2.167 |
[6] |
Ling Zhang, Xiaoqi Sun. Stability analysis of time-varying delay neural network for convex quadratic programming with equality constraints and inequality constraints. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022035 |
[7] |
Yanjun Wang, Shisen Liu. Relaxation schemes for the joint linear chance constraint based on probability inequalities. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021132 |
[8] |
Zhi-Bin Deng, Ye Tian, Cheng Lu, Wen-Xun Xing. Globally solving quadratic programs with convex objective and complementarity constraints via completely positive programming. Journal of Industrial and Management Optimization, 2018, 14 (2) : 625-636. doi: 10.3934/jimo.2017064 |
[9] |
Gang Li, Yinghong Xu, Zhenhua Qin. Optimality conditions for composite DC infinite programming problems. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022064 |
[10] |
Gang Li, Lipu Zhang, Zhe Liu. The stable duality of DC programs for composite convex functions. Journal of Industrial and Management Optimization, 2017, 13 (1) : 63-79. doi: 10.3934/jimo.2016004 |
[11] |
Ailing Zhang, Shunsuke Hayashi. Celis-Dennis-Tapia based approach to quadratic fractional programming problems with two quadratic constraints. Numerical Algebra, Control and Optimization, 2011, 1 (1) : 83-98. doi: 10.3934/naco.2011.1.83 |
[12] |
Songqiang Qiu, Zhongwen Chen. An adaptively regularized sequential quadratic programming method for equality constrained optimization. Journal of Industrial and Management Optimization, 2020, 16 (6) : 2675-2701. doi: 10.3934/jimo.2019075 |
[13] |
Yuying Zhou, Gang Li. The Toland-Fenchel-Lagrange duality of DC programs for composite convex functions. Numerical Algebra, Control and Optimization, 2014, 4 (1) : 9-23. doi: 10.3934/naco.2014.4.9 |
[14] |
Nan Zhang, Linyi Qian, Zhuo Jin, Wei Wang. Optimal stop-loss reinsurance with joint utility constraints. Journal of Industrial and Management Optimization, 2021, 17 (2) : 841-868. doi: 10.3934/jimo.2020001 |
[15] |
Yanjun Wang, Kaiji Shen. A new concave reformulation and its application in solving DC programming globally under uncertain environment. Journal of Industrial and Management Optimization, 2020, 16 (5) : 2351-2367. doi: 10.3934/jimo.2019057 |
[16] |
Amin Reza Kalantari Khalil Abad, Farnaz Barzinpour, Seyed Hamid Reza Pasandideh. A novel separate chance-constrained programming model to design a sustainable medical ventilator supply chain network during the Covid-19 pandemic. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2021234 |
[17] |
Gang Li, Xiaoqi Yang, Yuying Zhou. Stable strong and total parametrized dualities for DC optimization problems in locally convex spaces. Journal of Industrial and Management Optimization, 2013, 9 (3) : 671-687. doi: 10.3934/jimo.2013.9.671 |
[18] |
Qing Liu, Bingo Wing-Kuen Ling, Qingyun Dai, Qing Miao, Caixia Liu. Optimal maximally decimated M-channel mirrored paraunitary linear phase FIR filter bank design via norm relaxed sequential quadratic programming. Journal of Industrial and Management Optimization, 2021, 17 (4) : 1993-2011. doi: 10.3934/jimo.2020055 |
[19] |
Harald Held, Gabriela Martinez, Philipp Emanuel Stelzig. Stochastic programming approach for energy management in electric microgrids. Numerical Algebra, Control and Optimization, 2014, 4 (3) : 241-267. doi: 10.3934/naco.2014.4.241 |
[20] |
Yufeng Zhou, Bin Zheng, Jiafu Su, Yufeng Li. The joint location-transportation model based on grey bi-level programming for early post-earthquake relief. Journal of Industrial and Management Optimization, 2022, 18 (1) : 45-73. doi: 10.3934/jimo.2020142 |
2020 Impact Factor: 1.801
Tools
Metrics
Other articles
by authors
[Back to Top]