2010-06-04Buch DOI: 10.18452/8409
Reformulation of general chance constrained problems using the penalty functions
Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
We explore reformulation of nonlinear stochastic programs with several joint chance constraints by stochastic programs with suitably chosenpenalty-type objectives. We show that the two problems are asymptotically equivalent. Simpler cases with one chance constraint and particular penalty functions were studied in [5, 9]. The obtained problems with penalties and with a ﬁxed set of feasible solutions are simpler to solve and analyze then the chance constrained programs. We discuss solving both problems using Monte-Carlo simulation techniques for the cases when the set of feasible solution is ﬁnite or inﬁnite bounded. The approach is applied to the ﬁnancial optimization problem with Value at Risk constraint, transaction costs and integer allocations. We compare the ability to generate a feasible solution of the original chance constrained problem using the sample approximations of the chance constraints directly or via sample approximation of the penaltyfunction objective.
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