simkit.solvers.sqpmfem#

Functions#

sqp_mfem(p0, energy_func, hess_blocks_func, ...[, ...])

SQP solver for the MFEM system from https://www.dgp.toronto.edu/projects/subspace-mfem/ , Section 4.

Module Contents#

simkit.solvers.sqpmfem.sqp_mfem(p0, energy_func, hess_blocks_func, grad_blocks_func, tolerance=0.0001, max_iter=100, do_line_search=True, verbose=False)#

SQP solver for the MFEM system from https://www.dgp.toronto.edu/projects/subspace-mfem/ , Section 4.

The full system looks like:

[Hu 0 Gu] [du] - [fu] [0 Hz Gz] [dz] = - [fz] [Gz.T 0 0] [mu] - [fmu]

Where Gz is diagonal and easily invertible. Using this fact, we can rewrite the system into a small solve and a matrix mult

(Hu + Gu Gz^-1 Hz Gz^-1 Gu.T) du = -fu + Gu Gz^-1 fz - Gu Gz^-1 Hz Gz^-1 fmu dz = -Gz^-1 (fz + Hz du)

Parameters:

  • p0 ((n, 1) np.ndarray) – Initial guess for the stacked state.

  • energy_func (callable) – Energy function to minimize. Only used when do_line_search is True.

  • hess_blocks_func (callable) – Maps p to the hessian blocks Hu, Hz, Gu, Gz, Gzi.

  • grad_blocks_func (callable) – Maps p to the gradient blocks fu, fz, fmu.

  • tolerance (float) – Convergence tolerance on the norm of the gradient.

  • max_iter (int) – Maximum number of iterations.

  • do_line_search (bool) – If True, run a backtracking line search to pick the step size.

  • verbose (bool) – Unused placeholder for diagnostics.

Returns:

p – Minimizer estimate.

Return type:

(n, 1) np.ndarray