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Journal Article

Stochastic programming problems with generalized integrated chance constraints

Branda Martin

: Optimization vol.61, 8 (2012), p. 949-968

: GAP402/10/1610, GA ČR, 261315/2010, SVV

: chance constraints, integrated chance constraints, penalty functions, sample approximations, blending problem

: 10.1080/02331934.2011.587007

: programming problems with generalized integrated.pdf

(eng): 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.

: BB