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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 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.

Keywords: Active-set methods; Unit simplex; Non-convex optimization; Large-scale optimization

Category 1: Nonlinear Optimization

Citation: https://doi.org/10.1007/s10589-020-00195-x

Download: [PDF]

Entry Submitted: 03/22/2017
Entry Accepted: 03/22/2017
Entry Last Modified: 05/18/2020

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