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

Andrea Cristofari (), Marianna Santis (), Stefano Lucidi () and Francesco Rinaldi ()
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Andrea Cristofari: Università di Padova
Marianna Santis: Sapienza Università di Roma
Stefano Lucidi: Sapienza Università di Roma
Francesco Rinaldi: Università di Padova

Computational Optimization and Applications, 2020, vol. 77, issue 1, No 3, 57-89

Abstract: 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; 65K05; 90C06; 90C30 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10589-020-00195-x

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