Stochastic programming with incomplete information:a surrey of results on postoptimization and sensitivity analysis

Jitka Dupačová

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Risk and Portfolio Optimization Advanced Optimization Algorithms Research Probabilistic and Robust Engineering Design

Abstract

The possibility of successful applications of stochastic programming decision models has been limited by the assumed complete knowledge of the distribution Fof the random parameters as well as by the limited scope of the existing numerical procedures. We shall give a survey of selected methods which can be used to deal with the incomplete knowledge of the distribution F, namely to study robustness of the optimal solution and the optimal value of the objective function relative to small changes of the underlying distribution and to get error bounds in approximation schemes.

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References

1967Entscheidungskriterien bei Risiko 1960Inequalities for Stochastic Linear Programming Problems 1986Designing approximation schemes for stochastic optimization problems, in particular for stochastic programs with recourse 1983Stochastic Programming: Solution Techniques and Approximation Schemes 1987The minimax approach to stochastic programming and an illustrative application 1972More bounds on the expectation of a convex function of a random variable 1979Computational methods for solving two-stage stochastic linear programming problems 1982Solving Stochastic Programming Problems with Recourse Including Error Bounds

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1996Rates of Convergence in Stochastic Programs with Complete Integer Recourse 1993Stability of Solutions for Stochastic Programs with Complete Recourse 2000Decreasing the sensitivity of open-loop optimal solutions in decision making under uncertainty 2000Some Aspects of Stability in Stochastic Programming

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