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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), 401426. 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), 235263. 
[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), 14321457. 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), 617630. doi: 10.1287/opre.1100.0910. 
[7] 
R. Horst and N. V. Thoni, DC programming: Overview, J. Optim. Theory Appl., 103 (1999), 143. 
[8] 
D. Klatte and W. Li, Asymptotic constraint qualifications and global error bounds for convex inequalities, Math. Program., 84 (1999), 137160. 
[9] 
A. Nemirovski and A. Shapiro, Convex approximations of chance constrained programs, SIAM J. Optim., 17 (2006), 969996. 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), 401426. 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), 235263. 
[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), 14321457. 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), 617630. doi: 10.1287/opre.1100.0910. 
[7] 
R. Horst and N. V. Thoni, DC programming: Overview, J. Optim. Theory Appl., 103 (1999), 143. 
[8] 
D. Klatte and W. Li, Asymptotic constraint qualifications and global error bounds for convex inequalities, Math. Program., 84 (1999), 137160. 
[9] 
A. Nemirovski and A. Shapiro, Convex approximations of chance constrained programs, SIAM J. Optim., 17 (2006), 969996. 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. 
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