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An Active-Set Algorithmic Framework for Non-Convex Optimization Problems over the Simplex

Cristofari Andrea (andrea.cristofari***at***unipd.it)
De Santis Marianna (mdesantis***at***diag.uniroma1.it)
Lucidi Stefano (lucidi***at***diag.uniroma1.it)
Rinaldi Francesco (rinaldi***at***math.unipd.it)

Abstract: In this paper, we describe a new active-set algorithmic framework for minimizing a function over the simplex. The method, at each iteration, makes use of a rule for identifying active variables (i.e., variables that are zero at a stationary point) and a specific class of directions (so-called active-set gradient related directions) satisfying a new "nonorthogonality" type of condition that well suits to our needs. We prove convergence when using an Armijo line search in the given framework. We further describe three different active-set gradient related directions guaranteeing linear convergence of our framework (under suitable assumptions). Finally, we report numerical experiments showing the effectiveness of the approach.

Keywords: Active-set methods, Unit simplex

Category 1: Nonlinear Optimization


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Entry Submitted: 03/22/2017
Entry Accepted: 03/22/2017
Entry Last Modified: 06/01/2018

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