Download A Scenario Tree-Based Decomposition for Solving Multistage by Debora Mahlke PDF

By Debora Mahlke

Optimization difficulties concerning doubtful information come up in lots of parts of commercial and monetary functions. Stochastic programming presents an invaluable framework for modeling and fixing optimization difficulties for which a likelihood distribution of the unknown parameters is available.
prompted via functional optimization difficulties happening in strength structures with regenerative power offer, Debora Mahlke formulates and analyzes multistage stochastic mixed-integer versions. for his or her resolution, the writer proposes a singular decomposition procedure which is dependent upon the concept that of splitting the underlying state of affairs tree into subtrees. according to the formulated versions from power creation, the set of rules is computationally investigated and the numerical effects are discussed.

Show description

Read Online or Download A Scenario Tree-Based Decomposition for Solving Multistage Stochastic Programs: With Application in Energy Production PDF

Best probability & statistics books

Statistical Simulation: Power Method Polynomials and Other Transformations

Even though energy procedure polynomials according to the normal common distributions were utilized in many alternative contexts for the previous 30 years, it used to be no longer until eventually lately that the chance density functionality (pdf) and cumulative distribution functionality (cdf) have been derived and made on hand. concentrating on either univariate and multivariate nonnormal information new release, Statistical Simulation: energy procedure Polynomials and different modifications offers ideas for accomplishing a Monte Carlo simulation learn.

Stochastic Differential Equations, Backward SDEs, Partial Differential Equations

This examine monograph provides effects to researchers in stochastic calculus, ahead and backward stochastic differential equations, connections among diffusion tactics and moment order partial differential equations (PDEs), and fiscal arithmetic. It will pay distinct recognition to the relatives among SDEs/BSDEs and moment order PDEs below minimum regularity assumptions, and likewise extends these effects to equations with multivalued coefficients.

Stochastic differential equations and applications. Vol.1

This article develops the speculation of platforms of stochastic differential equations, and it provides functions in chance, partial differential equations, and stochastic regulate difficulties. initially released in volumes, it combines a e-book of uncomplicated thought and chosen subject matters with a booklet of functions.

Rare Event Simulation using Monte Carlo Methods

In a probabilistic version, an extraordinary occasion is an occasion with a really small likelihood of prevalence. The forecasting of infrequent occasions is an impressive activity yet is necessary in lots of components. for example a catastrophic failure in a delivery method or in a nuclear energy plant, the failure of a data processing approach in a financial institution, or within the conversation community of a gaggle of banks, resulting in monetary losses.

Extra info for A Scenario Tree-Based Decomposition for Solving Multistage Stochastic Programs: With Application in Energy Production

Sample text

The set A contains all arcs of the tree. In detail a scenario tree is given by a rooted tree with T layers, where each layer corresponds to a period t of the program. The root node n = 1 corresponds to time period t = 1 and t(n) denotes the time stage of node n. As Γ is a tree, each node n ∈ N has a unique predecessor p(n). Generalizing, the k-th predecessor of a node is denoted by pk (n). The set Nt contains all nodes of period t. Consequently, NT consists of all leaf nodes of Γ, which means that the corresponding nodes do not have a successor.

Likewise, the discharged power of discharging unit l ∈ Lj is described by sout lt ∈ R+ . For the description of the operational state of a unit k ∈ Kj , we introduce in ∈ {0, 1} and accordingly for a discharging unit the decision variable zkt in,up out ∈ {0, 1} and l ∈ Lj the variable zlt ∈ {0, 1}. The start-up variables zkt out,up ∈ {0, 1} indicate whether unit k ∈ Kj or l ∈ Lj is switched on in zlt time period t, respectively. In order to describe whether any unit of storage in ∈ {0, 1} j performs charging or discharging operations, the variables yjt out and yjt ∈ {0, 1} are introduced.

VT }. 6). Indeed, the deterministic switching polytope it is a special case of the stochastic switching polytope, where the scenario tree consists of a single path. 10) xup n ≥ 0, n for all n ∈ N \{1} and by T T xup vk − −xvT + k=i for i = 2, . . 11) xdown vk ≤ 1, for i = 2, . . , T − l + 1. 12) T xup vk + k=i+l ≤ 0, k=i+L T xvT − xdown vk k=i for all s ∈ S with corresponding path (v1 , . . , vT ). For these 2N − 2 + |S|(2T − L − l) inequalities, we show that they also define facets of the stochastic polytope PΓ,L,l .

Download PDF sample

Rated 4.36 of 5 – based on 20 votes