中文
Published date:2014-03-27    Provided by:
 
Title: Iterative Reweighted Minimization Methods for $l_p$ Regularized Unconstrained Nonlinear Programming
Guest SpeakerProfessor Lu Zhaosong, Department of Statistics and Actuarial Science at SFU
Time2014-1-3, 10:10 – 11:30
LocationSY202
Content &Introduction 
In this talk, we consider general $l_p$ regularized unconstrained minimization problems. In particular, we derive lower bounds for nonzero entries of the first- and second-order stationary points and hence also of local minimizers of the $l_p$ minimization problems. We extend some existing iterative reweighted $l_1$ (IRL1) and $l_2$ (IRL2) minimization methods to solve these problems and propose new variants for them in which each subproblem has a closed-form solution. Also, we provide a unified convergence analysis for these methods. In addition, we propose a novel Lipschitz continuous $/eps$-approximation to $/|x/|^p_p$. Using this result, we develop new IRL1 methods for the $l_p$ minimization problems and show that any accumulation point of the sequence generated by these methods is a first-order stationary point, provided that the approximation parameter $/epsilon$ is below a computable threshold value. This is a remarkable result since all existing iterative reweighted minimization methods require that $/epsilon$ be dynamically updated and approach zero. Our computational results demonstrate that the new IRL1 method and the new variants generally outperform the existing IRL1 methods.