19. Interior Point Sequential Linear-Quadratic Programming: KNITRO/INTERIOR

In Chapter 14 the KNITRO/ACTIVE algorithm based on the active-set sequential programming method has been presented. In this chapter the KNITRO/INTERIOR algorithm is being described, together with its numerical performances for solving large-scale general continuously nonlinear optimization problems. KNITRO/INTERIOR provides two procedures for computing the steps within the interior point approach. In the version INTERIOR-CG, each step is computed using a projected conjugate gradient iteration. It factors a projection matrix and uses the conjugate gradient method to approximately minimize a quadratic model of the barrier problem. In the version INTERIOR-DIRECT, the algorithm attempts to compute a new iterate by solving the primal-dual KKT system using direct linear algebra. In case this step cannot be guaranteed to be of good quality or if a negative curvature is detected, then the new iterate is computed by the INTERIOR-CG algorithm. The description of the KNITRO/INTERIOR-CG algorithm is given by Byrd et al. (1999), and its global convergence theory is presented by Byrd et al. (2000). The method implemented in the KNITRO/INTERIOR-DIRECT algorithm is described by Waltz et al. (2003).