Wednesday, 15:45 - 16:10 h, Room: MA 144

 

Zuzana ҆abartov√°
Spatial decomposition for differential equation constrained stochastic programs

Coauthor: Pavel Popela

 

Abstract:
When optimization models are constrained by ordinary or partial differential equations (ODE or PDE), numerical method based on discretising domain are required to obtain non-differential numerical description of the differential parts; we chose the finite element method. The real problems are often very large and exceed computational capacity. Hence, we employ the progressive hedging algorithm (PHA) - an efficient decomposition method for solving scenario-based stochastic programs - which can be implemented in parallel to reduce the computing time. A modified PHA was used for an original concept of spatial decomposition based on mesh created for approximating differential constraints. We solve our problem with raw discretization, decompose it into overlapping parts of the domain, and solve it again iteratively by PHA with finer discretization - using values from the raw discretization as boundary conditions - until a given accuracy is reached.
The spatial decomposition is applied to a civil engineering problem: design of beam cross section dimensions. The algorithms are implemented in GAMS and the results are evaluated by width of overlap and computational complexity.

 

Talk 2 of the contributed session Wed.3.MA 144
"Network design, reliability, and PDE constraints" [...]
Cluster 22
"Stochastic optimization" [...]

 

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