中文
Published date:2013-09-24    Provided by:
Guest Speaker: 陈小君教授

Time:

2012-05-16  16:00-18:00

Location School of Science Meeting Room
Content: 

.Minimization problems with non-Lipschitz, nonconvex regularization terms have wide applications in image restoration, signal reconstruction and variable selection. On ?2-?p (0 < p < 1) regularized minimization, we show that_nding a global optimal solution is strongly NP-hard. On the other hand, we present lower bounds of nonzero entries in every local optimal solution without assumptions on the data matrix. Such lower bounds can be used to classify zero and nonzero entries in local optimal solutions and select regularization parameters for desirable sparsity of solutions. We propose a smoothing quadratic regularization algorithm for unconstrained problems and a first-order interior point algorithm for box constrained problems and show the worst-case iteration complexity for finding an escaled first-order stationary point is O(e-2). Moreover, we develop a smoothing trust region Newton method and a second-order interior point algorithm for finding an esecond-order stationary point. Although the two second-order algorithms cost more computational time than that of the first-order algorithms in each iteration, the worst-case iteration complexity for finding an e(scaled) second-order stationary point is reduced to O(e-2/3). Examples are presented to illustrate the theory and algorithms.

Date Modified:2012-05-16