solver::numeric::finite_difference::elliptic::problem

Trait EllipticControlProblem

pub trait EllipticControlProblem<const N: usize>: ControlProblem<N> {
    // Required methods
    fn dimension_kind(&self, dim: usize) -> DimensionKind;
    fn transport(
        &self,
        state: &[f64; N],
        control: &Self::Control,
        derivs: &StateDerivatives<N>,
    ) -> Transport<N>;

    // Provided method
    fn boundary_conditions(&self) -> BoundaryConditions<N> { ... }
}

Expand description

A stationary (infinite-horizon) stochastic optimal control problem.

The stationary HJB equation is

0 = sup_u { f(x,u) + L^u V - r V }

where f is the running reward, L^u V is the controlled generator, and r is the discount rate. After optimizing over u, the equation is assembled in the same -T V + r V = source form as EllipticProblem, with T V + source = sup_u { f + L^u V }.

This trait extends crate::models::control::ControlProblem with the discretization data needed by the stationary finite-difference solver. The transport method has the same semantics as crate::numeric::finite_difference::pde::PdeProblem::transport: plus and minus define T, and source is the residual that makes T V + source equal the optimized driver.

Required Methods§

Source

fn dimension_kind(&self, dim: usize) -> DimensionKind

Discretization kind for dim.

Source

fn transport( &self, state: &[f64; N], control: &Self::Control, derivs: &StateDerivatives<N>, ) -> Transport<N>

Transport coefficients and residual source for the given control and derivatives.

The returned source is used as the right-hand side of the stationary operator. It must satisfy T V + source = f + L^u V at the current derivative bundle, where T V is the discrete transport operator built from plus and minus.