A regularized decomposition method for minimizing a sum of polyhedral functions
Mathematical Programming: Series A and B
Local epi-continuity and local optimization
Mathematical Programming: Series A and B
Stability in two-stage stochastic programming
SIAM Journal on Control and Optimization
Distribution sensitivity in stochastic programming
Mathematical Programming: Series A and B
Stability analysis for stochastic programs
Annals of Operations Research
Stochastic decomposition: an algorithm for two-state linear programs with recourse
Mathematics of Operations Research
Continuity properties of expectation functions in stochastic integer programming
Mathematics of Operations Research
Stability of solutions for stochastic programs with complete recourse
Mathematics of Operations Research
Stochastic programming with simple integer recourse
Mathematical Programming: Series A and B
Quantitative stability in stochastic programming
Mathematical Programming: Series A and B
On the expected value function of a simple integer recourse problem with random technology matrix
Journal of Computational and Applied Mathematics
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
Rates of Convergence in Stochastic Programs with Complete Integer Recourse
SIAM Journal on Optimization
Quantitative Stability in Stochastic Programming: The Method of Probability Metrics
Mathematics of Operations Research
A finite branch-and-bound algorithm for two-stage stochastic integer programs
Mathematical Programming: Series A and B
Introduction to Stochastic Programming
Introduction to Stochastic Programming
Dual decomposition in stochastic integer programming
Operations Research Letters
Heuristics for Multi-Stage Interdiction of Stochastic Networks
Journal of Heuristics
Operations Research
Discrete Applied Mathematics
Risk Averse Shape Optimization
SIAM Journal on Control and Optimization
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In the setting of stochastic recourse programs, we consider the problem of minimizing the probability of total costs exceeding a certain threshold value. The problem is referred to as the minimum risk problem and is posed in order to obtain a more adequate description of risk aversion than that of the accustomed expected value problem. We establish continuity properties of the recourse function as a function of the first-stage decision, as well as of the underlying probability distribution of random parameters. This leads to stability results for the optimal solution of the minimum risk problem when the underlying probability distribution is subjected to perturbations. Furthermore, an algorithm for the minimum risk problem is elaborated and we present results of some preliminary computational experiments.