Vaggelis Papoutsis authored Dec 07, 2023 and Andrew Heather committed Dec 18, 2023

The solution of the QP subproblem can become quite expensive, especially
for cases with many design variables (e.g. topology optimisation).

A (potentially dense) matrix with the size of the design variables is
solved using a matrix-free CG solver. The convergence speed greatly
depends on the used preconditioner. This commit adds
preconditioner-vector products based on the L-BFGS inverse Hessian and,
more importantly, a preconditioner computed using the Sherman-Morrison
formula. The latter is applicable here since the LHS of the QP problem
is computed as the sum of rank-2 L-BFGS updates, a sum of rank-1 updates
(as many as the flow-related constraints) and a diagonal matrix
depending on the bound constraints.

Additionally, the QP subproblem could have no feasible points. To relax
this, constraints can be applied gradually through the
targetConstraintReduction enty (typical value of 0.1 for topology
optimisation).