Download Stochastic Programming Methods and Technical Applications: by P. Kall (auth.), Prof. Dr. Kurt Marti, Prof. Dr. Peter Kall PDF
By P. Kall (auth.), Prof. Dr. Kurt Marti, Prof. Dr. Peter Kall (eds.)
Optimization difficulties bobbing up in perform often comprise a number of random parameters. for that reason, in an effort to receive optimum recommendations being strong with recognize to random parameter adaptations, the as a rule on hand statistical information regarding the random parameters could be thought of already on the making plans part. the unique challenge with random parameters has to be changed through a suitable deterministic alternative challenge, and effective numerical resolution or approximation suggestions need to be constructed for these difficulties. This complaints quantity encompasses a collection of papers on modelling ideas, approximation equipment, numerical answer systems for stochastic optimization difficulties and functions to the reliability-based optimization of concrete technical or financial systems.
Read Online 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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Additional 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,
Sample text
Compute a nominal decrease Q n = f{xn) - A{x) - ~ < Mn{x - xn),x - Xn > . A constant C E (O, 1) being chosen, we perform the descent test: f{x) ~ f{xn) - CQn If the inequality is satisfied we set Xn+1 = Xj Yk+l = x and increase n and k by 1. Otherwise, n is kept fixed, we set Yk+l = x and increase k by 1. In some versions (cf. [42]) an additional test is made before increasing k. 3. The choice of {Mn} given in the literature is: - an abstract sequence, as in [39], - Mn == I, as in [34], - Mn = /LnI with heuristic rules for computing /Ln, in [36], [64], - solving a quasi-Newton equation in [42].
Duality theorems for dynamic models that are relevant for our setting are considered in [56), [58). We utilize the results of [56). 1 ) for a moment. 1 )*. First, let us recall that the dynamic recourse problem has relatively complete recourse if the following procedure leads to a choice of decisions Xk, k = 1, ... , K, almost surely for all stages k: Let Xl be a feasible solution of the first stage. In the second stage (having a new observation of the load), we can choose X2 satisfying the constraints and the dynamics of the system, i.
In the second stage (having a new observation of the load), we can choose X2 satisfying the constraints and the dynamics of the system, i. 3 ) hold true with the corresponding components of Xl and X2. And so forth: In the k-th stage, we are able to choose a feasible decision X k . Nonanticipativity and relatively complete recourse provide sufficient conditions for considering Ll to be the space of Lagrange multipliers A, instead of working with esoteric objects from (Loo)* (cf. [56)). Suppose, additionally, that strict feasibility holds true.