Especially on fine space discretizations we obtain large scale quadratic subproblems (5.34) in the inexact SQP method described in Chapter 5. The goal of this chapter is to present a
approach which is one of two steps for the solution of these large scale QPs. It consists of a structure exploiting elimination of all discretized PDE variables from the QP. The resulting equivalent QP is of much smaller, grid-independent size and can then, in a second step, be solved by, e.g., a Parametric Active Set Method (PASM) which we describe in Chapter 9.
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