Quasi-Newton techniques are frequently used for the numerical solution of unconstrained and linearly or nonlinearly constrained optimization problems. The key computational step of these techniques is the updating of a symmetric positive definite matrix after a symmetric rank-two modification, involving an addition and a subtraction of dyads. Some inefficiencies and numerical difficulties may arise mainly due to the subtraction operation. The paper discusses efficient and stable quasi-Newton updates using various orthogonal and unitary transformations.
Cholesky factorization, downdating, matrix modifications, optimization, orthogonal transformations, quasi-Newton methods, updating.
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