Nonmonotone Spectral Gradient Method for l_1-regularized Least Squares

• DOI: 10.19139/soic.v4i3.230
• Publication Date: 2016-08-30T15:26:50Z
• Authors: Wanyou Cheng; Qingjie Hu
• Keywords: Karush–Kuhn–Tucker conditions; Regularization; Stationary point; Overdetermined system; Constrained optimization

In the paper, we investigate a linear constraint optimization reformulation to more general form of l_1 regularization problem and give some good properties it. We first show that equivalence between problem. Second, KKT point always exists since constraints are linear; half must be active at any point. addition, points same as stationary Based on problem, propose nonomotone spectral gradient method establish its global convergence. Numerical experiments with compressive sense problems our approach is competitive several known methods for standard l_2-l_1