Convergence of the reweighted ℓ <Subscript>1</Subscript> minimization algorithm for ℓ <Subscript>2</Subscript>–ℓ <Subscript> p </Subscript> minimization

The iteratively reweighted ℓ <Subscript>1</Subscript> minimization algorithm (IRL1) has been widely used for variable selection, signal reconstruction and image processing. In this paper, we show that any sequence generated by the IRL1 is bounded and any accumulation point is a stationary point of the ℓ <Subscript>2</Subscript>–ℓ <Subscript> p </Subscript> minimization problem with 0>p>1. Moreover, the stationary point is a global minimizer and the convergence rate is approximately linear under certain conditions. We derive posteriori error bounds which can be used to construct practical stopping rules for the algorithm. Copyright Springer Science+Business Media New York 2014