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Parameters, Variables and Settings

TwoStageOptimalControl.ParametersBasics — Function
ParametersBasics(Para,UserPara)

Initialize the basic parameters necessary for the model

  • T -> time horizon of the model
  • hstep -> time step between points
  • rho -> time discount rate of the model
  • nCon -> number of controls in the first stage
  • nCon_dist -> number of controls in the second stage
  • nStat -> number of state variables in the first stage
  • nStat_dist -> number of state variables in the second stage
  • ProbIndex -> index of state variable describing the auxiliary variables in both stages
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TwoStageOptimalControl.ParametersGrids — Function
ParametersGrids(Para,UserPara)

Initialize the parameters associated with the time grids

  • nTime -> Number of gridpoints along time
  • nAge -> Number of gridpoints along the vintages
  • tmesh -> Grid for time
  • amesh -> Grid for vintages
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TwoStageOptimalControl.ParametersControls — Function
ParametersControls(Para,UserPara)

Initialize the parameters associated with the control variables

  • LoadInits -> Loading specific initial guesses for the control variables
  • Reduce1 -> Indices of controls, which should be disabled (Stage 1)
  • Reduce2 -> Indices of controls, which should be disabled (Stage 2)
  • ConMin -> Lower bound for the concentated control variables
  • ConMax -> Upper bound for the concentated control variables
  • Con_distMin -> Lower bound for the distributed control variables
  • Con_distMax -> Upper bound for the distributed control variables
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TwoStageOptimalControl.ParametersAlgorithm — Function
ParametersAlgorithm(Para,UserPara)

Initialize the parameters for the optimisation algorithm

  • OptiType -> Adjustment of gradient of Hamiltonian
    • "Gradient" uses the standard gradient of the hamiltonian
    • "ProbAdjust" scales the gradient by the inverse of the auxiliary variables
    • "Newton-Raphson" scales the gradient by the inverse of the Hessian
  • IntegrationOrder -> Which order should the method of integration used should have.
    • 4 is the default using Simpson's rule
    • 2 is another option using the trapezoid rule
  • ParallelComputing -> Indicator whether calculations along vintages should be parallised. Needs to be implemented in the future.
  • hLowBound -> Lower bound for the step of the gridsize along time. hstep gets halfed until the new value falls below hLowBound.
  • InitLineStep -> Initial step-size for the adjustment of control variables along the gradient.
  • LineSearchStepIncrease -> Factor for increase in the linesearch stepsize.
  • UpperLineStep -> Upper bound for linesearch stepsize.
  • stepLowBound -> Lower bound for step in gradient search -> termination if undercut.
  • GradBound -> Lower bound for the gradient. Algorithm stops if maximum of the absolute value of the gradient is smaller.
  • MaxOptiIter -> Max iterations with same step-size h.
  • MaxLineIter -> Max iterations along the same gradient.
  • GradSmooth -> Indicator if gradients are smoothed.
  • ConSmooth -> Indicator if controls are smoothed.
  • SearchDISP -> Indicator if intermediate results of the search along the gradient shall be displayed.
  • LineIter -> Iteration counter
  • OptiIter -> Iteration counter
  • HstepIter -> Iteration counter
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TwoStageOptimalControl.ParametersInitStates — Function
ParametersInitStates(Para,UserPara)

Initialize initial and boundary data

  • InitStat -> Initial state values of concentated variables
  • InitStatdist -> Initial state values of distributed variables at t=t0 Will be used in future generalised version of the package
  • BoundStat_dist -> Initial state values of distributed variables at t Will be used in future generalised version of the package
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TwoStageOptimalControl.ParametersPlots — Function
ParametersPlots(Para,UserPara)

Initialize parameters relevant for plotting

  • nVintagePlot -> Number of vintages plotted for realtime solutions

  • PlotResultsStart -> Indicator for plot of initial guess

  • PlotResultsIntermediate -> Indicator for plot of intermediate results

  • PlotResultsFinal -> Indicator for plot of final results

  • PlotResultsIntermediateFrequency -> Number of algorithm iterations between plot of Intermediate results

  • PlotResultsWaitForKey -> Indicator whether user input of any key should be necessary after plot of intermediate results

  • SavePlot -> Indicator whether plotted results should be saved

  • SavePlotPath -> Path for saved plots

  • ControlLabelsLatex -> concentated control labels using latex strings

  • ControlLabelsSimple -> concentated control labels without latex strings

  • ControlDistLabelsLatex -> distributed control labels using latex strings

  • ControlDistLabelsSimple -> distributed control labels without latex strings

  • StateLabelsLatex -> concentated state labels using latex strings

  • StateLabelsSimple -> concentated state labels without latex strings

  • StateDistLabelsLatex -> distributed state labels using latex strings

  • StateDistLabelsSimple -> distributed state labels without latex strings

  • CoStateLabelsLatex -> concentated costate labels using latex strings

  • CoStateLabelsSimple -> concentated costate labels without latex strings

  • CoStateDistLabelsLatex -> distributed costate labels using latex strings

  • CoStateDistLabelsSimple -> distributed costate labels without latex strings

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