Nonlinear Optimization
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We consider an iterative computation of negative curvature directions, in large-scale unconstrained optimization frameworks, needed for ensuring the convergence toward stationary pointswhich satisfy second-order necessary optimality conditions. We show that to the latter purpose, we can fruitfully...
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The paper is concerned with multiobjective sparse optimization problems, i.e. the problem of simultaneously optimizing several objective functions and where one of these functions is the number of the non-zero components (or the ℓ-norm) of the solution. We propose to deal with the ℓ-norm by means...
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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 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...
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In this paper, we develop a new algorithmic framework to solve black-box problems with integer variables. The strategy included in the framework makes use of specific search directions (so called primitive directions) and a suitably developed nonmonotone line search, thus guaranteeing a high level...