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

Martin Branda — 2012

Kybernetika

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...

Local stability and differentiability of the Mean–Conditional Value at Risk model defined on the mixed–integer loss functions

Martin Branda — 2010

Kybernetika

In this paper, we study local stability of the mean-risk model with Conditional Value at Risk measure where the mixed-integer value function appears as a loss variable. This model has been recently introduced and studied in~Schulz and Tiedemann [16]. First, we generalize the qualitative results for the case with random technology matrix. We employ the contamination techniques to quantify a possible effect of changes in the underlying probability distribution on the optimal value. We use the generalized...

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