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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.
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. Google Scholar |
[3] |
Y. Gao, "Structured Low Rank Matrix Optimization Problems: A Penalty Approach,", Ph.D thesis, (2010). Google Scholar |
[4] |
Y. Gao and D. Sun, Calibrating least squares semidefinite programming with equality and inequality constraints,, SIAM J. Matrix Anal. Appl., 31 (2009), 1432.
doi: 10.1137/080727075. |
[5] |
M. Grant and S. Boyd, CVX: Matlab software for disciplined convex programming, version 1.21,, April, (2011). Google Scholar |
[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.
doi: 10.1287/opre.1100.0910. |
[7] |
R. Horst and N. V. Thoni, DC programming: Overview,, J. Optim. Theory Appl., 103 (1999), 1.
|
[8] |
D. Klatte and W. Li, Asymptotic constraint qualifications and global error bounds for convex inequalities,, Math. Program., 84 (1999), 137.
|
[9] |
A. Nemirovski and A. Shapiro, Convex approximations of chance constrained programs,, SIAM J. Optim., 17 (2006), 969.
doi: 10.1137/050622328. |
[10] |
R. T. Rockafellar, "Convex Analysis,", Princeton Mathematical Series, (1970).
|
[11] |
R. T. Rockafellar and R. J. B. Wets, "Variational Analysis,", Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 317 (1998).
|
[12] |
A. Shapiro, D. Dentcheva and A. Ruszczyński, "Lectures on Stochastic Programming: Modeling and Theory,", MPS/SIAM Series on Optimization, 9 (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.
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. Google Scholar |
[3] |
Y. Gao, "Structured Low Rank Matrix Optimization Problems: A Penalty Approach,", Ph.D thesis, (2010). Google Scholar |
[4] |
Y. Gao and D. Sun, Calibrating least squares semidefinite programming with equality and inequality constraints,, SIAM J. Matrix Anal. Appl., 31 (2009), 1432.
doi: 10.1137/080727075. |
[5] |
M. Grant and S. Boyd, CVX: Matlab software for disciplined convex programming, version 1.21,, April, (2011). Google Scholar |
[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.
doi: 10.1287/opre.1100.0910. |
[7] |
R. Horst and N. V. Thoni, DC programming: Overview,, J. Optim. Theory Appl., 103 (1999), 1.
|
[8] |
D. Klatte and W. Li, Asymptotic constraint qualifications and global error bounds for convex inequalities,, Math. Program., 84 (1999), 137.
|
[9] |
A. Nemirovski and A. Shapiro, Convex approximations of chance constrained programs,, SIAM J. Optim., 17 (2006), 969.
doi: 10.1137/050622328. |
[10] |
R. T. Rockafellar, "Convex Analysis,", Princeton Mathematical Series, (1970).
|
[11] |
R. T. Rockafellar and R. J. B. Wets, "Variational Analysis,", Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 317 (1998).
|
[12] |
A. Shapiro, D. Dentcheva and A. Ruszczyński, "Lectures on Stochastic Programming: Modeling and Theory,", MPS/SIAM Series on Optimization, 9 (2009).
|
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