An active set algorithmic framework for non convex optimization problems over the simplex
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.
Comput. Optim. Appl.