0381903 - ÚTIA 2013 RIV DE eng J - Journal Article
Branda, Martin
Stochastic programming problems with generalized integrated chance constraints.
Optimization. Roč. 61, č. 8 (2012), s. 949-968. ISSN 0233-1934. E-ISSN 1029-4945
R&D Projects: GA ČR GAP402/10/1610
Grant - others:SVV(CZ) 261315/2010
Institutional support: RVO:67985556
Keywords : chance constraints * integrated chance constraints * penalty functions * sample approximations * blending problem
Subject RIV: BB - Applied Statistics, Operational Research
Impact factor: 0.707, year: 2012 ; AIS: 0.469, rok: 2012
Result website:
http://library.utia.cas.cz/separaty/2012/E/branda-stochastic programming problems with generalized integrated.pdf

DOI: https://doi.org/10.1080/02331934.2011.587007

If the constraints in an optimization problem are dependent on a random parameter, we would like to ensure that they are fulfilled with a high level of reliability. The most natural way is to employ chance constraints. However, the resulting problem is very hard to solve. We propose an alternative formulation of stochastic programs using penalty functions. The expectations of penalties can be left as constraints leading to generalized integrated chance constraints, or incorporated into the objective as a penalty term. We show that the penalty problems are asymptotically equivalent under quite mild conditions. We discuss applications of sample-approximation techniques to the problems with generalized integrated chance constraints and propose rates of convergence for the set of feasible solutions. We will direct our attention to the case when the set of feasible solutions is finite, which can appear in integer programming. The results are then extended to the bounded sets with continuous variables.
Permanent Link: http://hdl.handle.net/11104/0212269