| Title:
|
Chance constrained problems: penalty reformulation and performance of sample approximation technique (English) |
| Author:
|
Branda, Martin |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
48 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
|
105-122 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
chance constrained problems |
| Keyword:
|
penalty functions |
| Keyword:
|
asymptotic equivalence |
| Keyword:
|
sample approximation technique |
| Keyword:
|
investment problem |
| MSC:
|
62A10 |
| MSC:
|
93E12 |
| idZBL:
|
Zbl 1243.93117 |
| idMR:
|
MR2932930 |
| . |
| Date available:
|
2012-03-05T08:33:36Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142065 |
| . |
| Reference:
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