Globally convergent primal-dual active-set methods with inexact subproblem solves (Q2832889)

In this paper, the authors propose various Primal-Dual Active-Set (PDAS) (i.\,e. sets where the constraints are equal to zero) methods for solving large-scale models of an important class of quadratic optimization problems (QPs). Algorithm 1: General PDAS framework. Algorithm 2: PDAS framework with inexact subspace solution. Algorithm 3: PDAS framework with inexact subspace solutions (dynamic). Algorithm 4 (variant of algorithm 3): PDAS framework with inexact subspace solutions (dynamic). The proof of convergence is postponed to the appendix, and is based on Karush-Kuhn-Tucker optimality conditions for QPs. The algorithms are implemented and numerical results are provided. The striking feature of these algorithms is that the reduced linear systems involved in the computation may be solved inexactly.