Matrix Updates for the Block Structured Factorization
The ability to update the Karush–Kuhn–Tucker (KKT) system’s factorization after addition or deletion of a constraint or simple bound is of vital importance for the efficiency of any active–set method, as described in section 6.3. The Hessian Projection Schur Complement (HPSC) factorization of the KKT system introduced in the previous chapter combines block local TQ decompositions, Cholesky decompositions, and Schur complements. A block tridiagonal Cholesky decomposition of the remaining symmetric positive definite system completes the factorization. In [201, 202, 203] a closely related factorization was used in an interior–point method. These methods typically perform few but expensive iterations using a modification of the KKT system of the entire Quadratic Program’s in each iteration, and thus by design do not require matrix updates.
KeywordsNull Space Cholesky Decomposition Cholesky Factor Point Constraint Tridiagonal System
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