Chance constrained problems: penalty reformulation and performance of sample approximation technique

0376766 - ÚTIA 2013 RIV CZ eng J - Journal Article
Branda, Martin
Chance constrained problems: penalty reformulation and performance of sample approximation technique.
Kybernetika. Roč. 48, č. 1 (2012), s. 105-122. ISSN 0023-5954
R&D Projects: GA ČR(CZ) GBP402/12/G097
Institutional research plan: CEZ:AV0Z10750506
Keywords : chance constrained problems * penalty functions * asymptotic equivalence * sample approximation technique * investment problem
Subject RIV: BB - Applied Statistics, Operational Research
Impact factor: 0.619, year: 2012
http://library.utia.cas.cz/separaty/2012/E/branda-chance constrained problems penalty reformulation and performance of sample approximation technique.pdf

We explore reformulation of nonlinear stochastic programs with several joint chance constraints by stochastic programs with suitably chosen penalty-type objectives. We show that the two problems are asymptotically equivalent. Simpler cases with one chance constraint and particular penalty functions were studied in [6,11]. 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 a 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 penalty function objective.
Permanent Link: http://hdl.handle.net/11104/0209085