By P. Kall (auth.), Prof. Dr. Kurt Marti, Prof. Dr. Peter Kall (eds.)
Optimization difficulties coming up in perform frequently include numerous random parameters. as a result, to be able to receive optimum options being powerful with admire to random parameter diversifications, the typically to be had statistical information regarding the random parameters might be thought of already on the making plans part. the unique challenge with random parameters has to be changed via a suitable deterministic replacement challenge, and effective numerical resolution or approximation strategies must be constructed for these difficulties. This lawsuits quantity encompasses a number of papers on modelling recommendations, approximation tools, numerical answer tactics for stochastic optimization difficulties and purposes to the reliability-based optimization of concrete technical or fiscal systems.
Read or Download Stochastic Programming Methods and Technical Applications: Proceedings of the 3rd GAMM/IFIP-Workshop on “Stochastic Optimization: Numerical Methods and Technical Applications” held at the Federal Armed Forces University Munich, Neubiberg/München, Germany, PDF
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Extra resources for Stochastic Programming Methods and Technical Applications: Proceedings of the 3rd GAMM/IFIP-Workshop on “Stochastic Optimization: Numerical Methods and Technical Applications” held at the Federal Armed Forces University Munich, Neubiberg/München, Germany,
Recent publications ,  suggest heuristics based on relaxed convexified primal problems These procedures are not directly applicable to the problem considered here due to the presence of pumped-storage hydro plants. An adaptation of these ideas to our setting needs further investigation. In our case, the Lagrangian heuristics could work as follows: • try to satisfy the reserve-constraints by using pumped-storage hydro plants in those time intervals, where the largest values of df + rt occur.
These statistical data provide a basis for the development of stochastic models for the load process and the optimization of power scheduling. Next we decribe two stochastic models for the optimal scheduling of electric power which differ mainly in the quality of available information on the load stochasticity. The first one represents a model for the optimal on-line or short-term operation of a power system, where future consequences of actual scheduling decisions as well as the future load uncertainty are taken into account.
Therefore, any method of non-smooth optimization of those discussed in the previous section could be applied. The methods developed as bundle methods of order higher than one could be applied successfully, e. g. , , . Unfortunately, for those guaranteeing superlinear convergence (), no computational code is available up to now. The variable metric bundle methods , ,  provide convergence but no estimate of the rate is given. We would like to emphasize that those methods are finite for piecewise linear convex functions.