Function pmcore::routines::evaluation::ipm::burke

source · 
pub fn burke(
    psi: &ArrayBase<OwnedRepr<f64>, Dim<[usize; 2]>>,
) -> Result<(ArrayBase<OwnedRepr<f64>, Dim<[usize; 1]>>, f64)>
Expand description

Applies the Burke’s Interior Point Method (IPM) to solve a specific optimization problem.

The Burke’s IPM is an iterative optimization technique used for solving convex optimization problems. It is applied to a matrix psi, iteratively updating variables and calculating an objective function until convergence.

The objective function to maximize is: f(x) = Σ(log(Σ(ψ_ij * x_j))) for i = 1 to n_sub

Subject to the constraints:

  1. x_j >= 0 for all j = 1 to n_point
  2. Σ(x_j) = 1 for j = 1 to n_point

Where:

  • ψ is an n_sub x n_point matrix with non-negative entries.
  • x is a probability vector of length n_point.

§Arguments

  • psi - A reference to a 2D Array representing the input matrix for optimization.

§Returns

A Result containing a tuple with two elements:

  • lam - An Array1<f64> representing the solution of the optimization problem.
  • obj - A f64 value representing the objective function value at the solution.

§Errors

This function returns an error if any of the optimization steps encounter issues. The error type is a boxed dynamic error (Box<dyn error::Error>).

§Example

Note: This function applies the Interior Point Method (IPM) to iteratively update variables until convergence, solving the convex optimization problem.