Factorization caching

[charleskhazoom]

Can OSQP do factorization caching of the KKT system if only parts of the $P$ and $A$ and rho matrices change when solving a new QP ? Or does factorization caching only work when vectors $q$, $l$ and $u$ change ?

[goulart-paul]

Factorization caching only works in OSQP if P and A do not change. If you change an element of either then you need to completely refactor the KKT system.

Note that by "completely refactor" I mean only the numerical factorisation. If you change elements of P and A, but only in places that were already in structural nonzeros, then you still make a saving on the symbolic factorisation and memory allocation phases since the factorisation of the KKT matrix keeps the same sparsity pattern.