Path-following interior point method: Theory and applications for the Stokes flow with a stick-slip boundary condition

Abstract

A path-following interior point method is proposed for minimization of quadratic functions subject to box and equality constraints. The problems with the singular Hessian that is symmetric, positive definite on the null space of the equality constraint matrix are considered. The inner linear systems are solved by the projected conjugate gradient method preconditioned by oblique projectors. Numerical experiments include large-scale problems arising from the TFETI domain decomposition method applied for solving the Stokes flow with the stick-slip boundary condition.