<p style='text-indent:20px;'>Total generalization variation (TGV) is a very powerful and important regularization for various inverse problems computer vision tasks. In this paper, we propose semismooth Newton based augmented Lagrangian method solving problem. The (also called as of multipliers) widely used lots smooth or nonsmooth variational problems. However, its efficiency heavily dep...

We discuss a globalization scheme for a class of active-set Newton methods for solving the mixed complementarity problem (MCP), which was proposed by the authors in [3]. The attractive features of the local phase of the method are that it requires solving only one system of linear equations per iteration, yet the local superlinear convergence is guaranteed under extremely mild assumptions, in p...

We consider concave minimization problems over nonconvex sets. Optimization problems with this structure arise in sparse principal component analysis. We analyze both a gradient projection algorithm and an approximate Newton algorithm where the Hessian approximation is a multiple of the identity. Convergence results are established. In numerical experiments arising in sparse principal component...

In an abstract framework, we study local convergence properties of Newton’s method for a sequence of generalized equations which models a discretized variational inequality. We identify conditions under which the method is locally quadratically convergent, uniformly in the discretization. Moreover, we show that the distance between the Newton sequence for the continuous problem and the Newton s...

This paper presents a parameterized Newton method using generalized Jacobians and a Broyden-like method for solving nonsmooth equations. The former ensures that the method is well-deened even when the generalized Jacobian is singular. The latter is constructed by using an approximation function which can be formed for nonsmooth equations arising from partial diierential equations and nonlinear ...