## Smoothing fast iterative hard thresholding algorithm for $\ell_0$ regularized nonsmooth convex regression problem

We investigate a class of constrained sparse regression problem with cardinality penalty, where the feasible set is defined by box constraint, and the loss function is convex, but not necessarily smooth. First, we put forward a smoothing fast iterative hard thresholding (SFIHT) algorithm for solving such optimization problems, which combines smoothing approximations, extrapolation techniques and … Read more

## On local non-global minimizers of quadratic optimization problem with a single quadratic constraint

In this paper, we consider the nonconvex quadratic optimization problem with a single quadratic constraint. First we give a theoretical characterization of the local non-global minimizers. Then we extend the recent characterization of the global minimizer via a generalized eigenvalue problem to the local non-global minimizers. Finally, we use these results to derive an efficient … Read more

## Gradient Descent only Converges to Minimizers

We show that gradient descent converges to a local minimizer, almost surely with random initialization. This is proved by applying the Stable Manifold Theorem from dynamical systems theory. Article Download View Gradient Descent only Converges to Minimizers

## Descent heuristics for unconstrained minimization

Semidefinite relaxations often provide excellent starting points for nonconvex problems with multiple local minimizers. This work aims to find a local minimizer within a certain neighborhood of the starting point and with a small objective value. Several approaches are motivated and compared with each other. Citation Report, Mathematisches Institut, Universitaet Duesseldorf, August 2008. Article Download … Read more