On the Convergence of Inexact Alternate Minimization in Problems with ℓ0 Penalties
Matteo Lapucci,
Alessio Sortino
Abstract:In this work, we consider unconstrained nonlinear optimization problems where the objective function presents a penalty term on the cardinality of a subset of the variables vector; specifically, we prove that an alternate minimization scheme has global asymptotic convergence guarantees towards points satisfying first order optimality conditions, even when the optimization step with respect to one of the blocks of variables is inexact and without introducing proximal terms. This result, supported by numerical e… Show more
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