A SMOOTHING MAJORIZATION METHOD FOR $l_2$-$l_p$ MATRIX MINIMIZATION
Abstract: We discuss the $l_2$-$l_p$ (with $p\in (0,1)$ matrix minimization for recovering low rank matrix. A smoothing approach is developed for solving this non-smooth, non-Lipschitz and non-convex optimization problem, in which the smoothing parameter is used as a variable and a majorization method is adopted to solve the smoothing problem. The convergence theorem shows that any accumulation point of the sequence generated by the smoothing approach satisfies the necessary optimality condition for the $l_2$-$l_p$ problem. As an application, we use the proposed smoothing majorization method to solve matrix competition problems. Numerical experiments indicate that our method is very efficient for obtaining the high quality recovery solution for matrix competition problems.
Keywords: Low rank problem, $l_2$-$l_p$ minimization, majorization method, lower bound analysis, smoothing method.
Category 1: Convex and Nonsmooth Optimization
Category 2: Linear, Cone and Semidefinite Programming
Entry Submitted: 01/20/2013
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