I am trying to implement a qp solver using interior point algorithm (Mehrotra Predictor-Corrector). In computing the affine directions, the Jacobian can be semidefinite (matlab warns in solving the linear system), what should I do for these cases? Will pseudo-inverse work? Thanks!
2026-03-25 09:31:28.1774431088
How to handle singular jacobian in interior point algorithm?
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This is a well-known problem in primal-dual interior point methods. In practice, one typically sets the corresponding entry in the Cholesky factor to a large positive value (effectively forcing the corresponding entry in $\Delta y$ to zero.)
You can find a good discussion of this issue and various methods for dealing with the problem in Chapter 11 of Stephen J. Wright's book, Primal-Dual Interior-Point Methods.