- Iterative Reweighted Minimization Methods for $l_p$ Regularized Unconstrained Nonlinear Programming Zhaosong Lu (zhaosongsfu.ca) Abstract: In this paper we study general $l_p$ regularized unconstrained minimization problems. In particular, we derive lower bounds for nonzero entries of 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 proposed 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 $\epsilon$-approximation to $\|x\|^p_p$. Using this result, we develop new IRL1 methods for the $l_p$ minimization problems and showed 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 is generally more stable than the existing IRL1 methods [21,18] in terms of objective function value and CPU time. Keywords: $l_p$ minimization, iterative reweighted $l_1$ minimization, iterative reweighted $l_2$ minimization Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization ) Category 2: Nonlinear Optimization (Unconstrained Optimization ) Citation: Manuscript, Department of Mathematics, Simon Fraser University, September 2012. Download: [PDF]Entry Submitted: 09/28/2012Entry Accepted: 09/28/2012Entry Last Modified: 10/06/2012Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.