Probabilistic Constrained Optimization - Part I of II

10:45 AM-12:45 PM

*Room: Atlanta 5*

For Part II, see MS31.

Optimization problems with probabilistic performance functions and constraints play an important role in several applications, such as, nuclear safety (core melt probability), ecology (extinction probability), environment (95% estimates of allowed doze), and finance (value-at-risk). Although these problems are very important, they attract relatively little interest from the optimization community because of their complexity. Recently, significant advances have been made in optimization and sensitivity analysis of the probabilistic functions, which is the basis for construction of new efficient optimization approaches. For instance, analytical formulas for the derivatives of probability functions have been developed and applied in Probabilistic Risk Analysis. The speakers in this minisymposium will present the state-of-the-art in probabilistic constrained optimization.

**Organizer: Stanislav Uryasev**

*University of Florida*

**10:45-11:10 Simulataneous Calculation of Sensitivities of Value-at-Risk Using Monte-Carlo and Numerical**- MethodsStanislav Uryasev, Organizer
**11:15-11:40 The Use of Discrete Moment Bounds in Probabilistic Constrained Stochastic Programming Models**

- András Prékopa, Rutgers University

**11:45-12:10 On Stochastic Integer Programming Problems Under Probabilistic Constraints**

*Darinka Dentcheva*, András Prékopa, and A. Ruszczynski, Rutgers University

**CANCELLED**~~12:15-12:40 Discrete Approximation of a Linear Two-stage Problem with Quantile Function~~

~~Andrei Kibzun, Moscow State Aviation Institute, Russia~~

*MMD, 3/15/99*