A Semismooth Newton-CG Method for Constrained Parameter Identification in Seismic Tomography

A Semismooth Newton-CG Dual Proximal Point Algorithm for Matrix Spectral Norm Approximation Problems

We consider a class of matrix spectral norm approximation problems for finding an affine combination of given matrices having the minimal spectral norm subject to some prescribed linear equality and inequality constraints. These problems arise often in numerical algebra, engineering and other areas, such as finding Chebyshev polynomials of matrices and fastest mixing Markov chain models. Based ...

Semismooth Newton and Quasi-Newton Methods in Weighted l−Regularization of Nonlinear Inverse Problems

In this paper, we investigate the semismooth Newton and quasi-Newton methods for the minimization problem in the weighted `−regularization of nonlinear inverse problems. We propose the conditions for obtaining the convergence of two methods. The semismooth Newton method is proven to locally converge with superlinear rate and the semismooth quasi-Newton method is proven to locally converge at le...

SDPNAL \(+\) : a majorized semismooth Newton-CG augmented Lagrangian method for semidefinite programming with nonnegative constraints

Abstract In this paper, we present a majorized semismooth Newton-CG augmented Lagrangian method, called SDPNAL+, for semidefinite programming (SDP) with partial or full nonnegative constraints on the matrix variable. SDPNAL+ is a much enhanced version of SDPNAL introduced by Zhao et al. (SIAM J Optim 20:1737–1765, 2010) for solving generic SDPs. SDPNAL works very efficiently for nondegenerate S...

A Semismooth Newton Method for Nonlinear Parameter Identification Problems with Impulsive Noise

A Newton-CG Augmented Lagrangian Method for Semidefinite Programming

We consider a Newton-CG augmented Lagrangian method for solving semidefinite programming (SDP) problems from the perspective of approximate semismooth Newton methods. In order to analyze the rate of convergence of our proposed method, we characterize the Lipschitz continuity of the corresponding solution mapping at the origin. For the inner problems, we show that the positive definiteness of th...