Semidefinite Programming For Chance Constrained Optimization Over Semialgebraic Sets

@article{Jasour2015SemidefinitePF,
  title={Semidefinite Programming For Chance Constrained Optimization Over Semialgebraic Sets},
  author={A. M. Jasour and Necdet Serhat Aybat and Constantino M. Lagoa},
  journal={SIAM Journal on Optimization},
  year={2015},
  volume={25},
  pages={1411-1440}
}
In this paper, “chance optimization” problems are introduced, where one aims at maximizing the probability of a set defined by polynomial inequalities. These problems are, in general, nonconvex and computationally hard. With the objective of developing systematic numerical procedures to solve such problems, a sequence of convex relaxations based on the theory of measures and moments is provided, whose sequence of optimal values is shown to converge to the optimal value of the original problem… CONTINUE READING