Nonlinear Optimization
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We introduce a class of positive definite preconditioners for the solution of large symmetric indefinite linear systems or sequences of such systems, in optimization frameworks. The preconditioners are iteratively constructed by collecting information on a reduced eigenspace of the indefinite...
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In this work, we deal with Truncated Newton methods for solving large scale (possibly nonconvex) unconstrained optimization problems. In particular,we consider the use of amodified Bunch and Kaufman factorization for solving the Newton equation, at each (outer) iteration of the method. The Bunch...
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In the context of augmented Lagrangian approaches for solving semidefinite programming problems, we investigate the possibility of eliminating the positive semidefinite constraint on the dual matrix by employing a factorization. Hints on how to deal with the resulting unconstrained maximization of...