In this paper, we describe a new active-set algorithmic framework for minimizing a non-convex function over the unit simplex. At each iteration, the method makes use of a rule for identifying active variables (i.e., variables that are zero at a stationary point) and specific directions (that we name active-set gradient related directions) satisfying a new “nonorthogonality” type of condition. We prove global convergence to stationary points when using an Armijo line search in the given framework. We further describe three different examples of active-set gradient related directions that guarantee linear convergence rate (under suitable assumptions). Finally, we report numerical experiments showing the effectiveness of the approach.

An active-set algorithmic framework for non-convex optimization problems over the simplex / Cristofari, A.; De Santis, M.; Lucidi, S.; Rinaldi, F.. - In: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. - ISSN 0926-6003. - (2020). [10.1007/s10589-020-00195-x]

An active-set algorithmic framework for non-convex optimization problems over the simplex

Cristofari A.
;
De Santis M.;Lucidi S.;
2020

Abstract

In this paper, we describe a new active-set algorithmic framework for minimizing a non-convex function over the unit simplex. At each iteration, the method makes use of a rule for identifying active variables (i.e., variables that are zero at a stationary point) and specific directions (that we name active-set gradient related directions) satisfying a new “nonorthogonality” type of condition. We prove global convergence to stationary points when using an Armijo line search in the given framework. We further describe three different examples of active-set gradient related directions that guarantee linear convergence rate (under suitable assumptions). Finally, we report numerical experiments showing the effectiveness of the approach.
2020
Active-set methods; Large-scale optimization; Non-convex optimization; Unit simplex
01 Pubblicazione su rivista::01a Articolo in rivista
An active-set algorithmic framework for non-convex optimization problems over the simplex / Cristofari, A.; De Santis, M.; Lucidi, S.; Rinaldi, F.. - In: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. - ISSN 0926-6003. - (2020). [10.1007/s10589-020-00195-x]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1403843
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