Optimization Online


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

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society