A Second Order Algorithm for MCP Regularized Optimization

In this article, we provide two optimal property of MCP regularization optimization. One shows that the support set of a local minimizer corresponds to linearly independent columns of $A$ , the other provides two sufficient conditions for a stationary point to be a local minimizer point. An active set subspace second-order algorithm for MCP regularized optimization is proposed. The active sets are estimated by an identification technique that can accurately identify the zero components in a neighbourhood of a stationary point. The search direction consists of two parts: some of the components are simply defined; the other components are determined by a second-order algorithm. A nonmonotone line search strategy that guarantees global convergence is used. The numerical comparisons with several state-of-art methods demonstrate the efficiency of the proposed method.