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SUMMARY:CAA Talk: Probabilistic Constrained Optimization on Flow Netwo
 rks (Schuster\, FAU)
UID:712b4d37-ab50-4405-8908-512f7bfa355e
DESCRIPTION:Probabilistic Constrained Optimization on Flow Networks Mi
 chael Schuster\, FAU\, Department Mathematik Abstract: Uncertainty oft
 en plays an important role in dynamic flow problems. In this paper\, w
 e consider both\, a stationary and a dynamic flow model with uncertain
  boundary data on networks. We introduce two different ways how to com
 pute the probability for random boundary data to be feasible\, discuss
 ing their advantages and disadvantages. In this context\, feasible mea
 ns\, that the flow corresponding to the random boundary data meets som
 e box constraints at the network junctions. The first method is the sp
 heric radial decomposition and the second method is a kernel density e
 stimator to compute the density of the solution at the nodes. In both 
 settings\, we consider certain optimization problems and we compute th
 e derivative of the probabilistic constraint using the kernel density 
 estimator. Moreover\, we derive necessary optimality conditions for th
 e stationary and the dynamic case. Throughout the paper\, we use numer
 ical examples to illustrate our results by comparing them with a class
 ical Monte Carlo approach to ompute the desired probability. Key-words
 : Stochastic Optimization\, Probabilistic Constraints\, Uncertain Boun
 dary Data\, Spheric-Radial Decomposition\, Kerne-Density Estimator\, F
 low Networks\, Gas Networks\, Contamination of Water https://en.www.ma
 th.fau.de/applied-analysis/caa-talks/
DTSTART:20200218T090000Z
DTEND:20200218T093000Z
LOCATION:03.323 Besprechungsraum CAA
DTSTAMP:20260723T051221Z
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