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Two new approximate formulations to joint chance-constrained optimization problems are proposed in this paper.The relationships of CVa R(conditional-value-at-risk),chance constrains and robust optimization are reviewed.Firstly,two new upper bounds on E((·)+)are proposed,where E stands for the expectation and x+=max(0,x),based on which two approximate formulations for individual chance-constrained problems are derived.The approximations are proved to be the robust optimization with the corresponding uncertain sets.Then the approximations are extrapolated to joint chance-constrained problem.Finally numerical studies are performed to compare the solutions of individual and joint chance constraints approximations and the results demonstrate the validity of our method.
Two new approximate formulations to joint chance-constrained optimization problems are proposed in this paper. The relationships of CVa R (conditional-value-at-risk), chance constrains and robust optimization are reviewed. Firstly, two new upper bounds on E (( ·) +) Are proposed, where E stands for the expectation and x + = max (0, x), based on which two approximate formulations for individual chance-constrained problems are derived. Approximations are proved to be the robust optimization with the corresponding unfounded sets.Then the approximations are extrapolated to joint chance-constrained problem. Finally numerical studies are performed to compare the solutions of individual and joint chance constraints approximations and the results demonstrate the validity of our method.