SPDPS

SPDPS is a Julia project providing the code for the PhD thesis A Stochastic Primal-Dual Proximal Splitting Method for Risk-Averse Optimal Control of PDEs by Sebastian Angerhausen, submitted in 2022 to the Faculty of Mathematics, University of Duisburg-Essen.

Usage

In order to use the project, you can follow the steps explained here. You basically need to

• download the code, start the Julia REPL and cd to the project directory,
• enter the package manager by pressing ],
• activate the project by executing the command activate .,
• for the first time use: instantiate the project by executing the command instantiate,
• exit the package manager by pressing backspace,
• load the project by executing using SPDPS.

Note that, in order to use the plotting features, you need to have Python installed together with the library matplotlib. For further help, see the installation instructions of PyPlot.jl.

You can then solve one of the two exemplary problems presented in the aforementioned PhD thesis by executing

run_test("EEDC")

for the elliptic equation with a discontinuous coefficient (see Section 6.3), and

run_test("SBE")

for the steady Burgers’ equation (see Section 6.4). The method run_test moreover takes the following keyword arguments:

• N: number of grid points
• S: number of scenarios
• β: probability level of CVaR
• risk_neutral: determines whether to compute a risk-neutral control or not
• tol: tolerance for the stopping criterion
• step_size: step size rule (either "constant" or "acc" for acceleration)
• σ: initial dual step size
• γ: acceleration parameter
• it_acc: number of iterations with acceleration
• CGF_rule: determines the index selection rule (1 or 2), 0 for no CGF
• q: parameter for the index selection
• use_Bk: determines whether to use the index set Bₖ or not
• maxit: maximum number of iterations
• it_out: defines after how many iterations the output is printed
• plot: determines whether to display plots or not
• csv: determines whether to create csv-files or not
• folder: name of the folder for output files
• tol_newton: tolerance for Newton's method (only for SBE)
• maxit_newton: maximum number of iterations for Newton's method (only for SBE)

The parameters N, S, β, tol, and q can be provided as arrays in order to compute solutions for all parameter combinations in a row.

If csv is true (which is the default value), then the results are automatically saved to csv-files that are located within a folder (with the name specified in folder) of the current working directory.