As a tractable approach, regularization is frequently adopted in sparse optimization. This gives rise to regularized optimization, which aims minimize the ?0 norm or its continuous surrogates that characterize sparsity. From continuity of discreteness norm, most challenging model ?0-regularized There an impressive body work on development numerical algorithms overcome this challenge. However, d...

Calibration estimation is currently the most popular method of estimation using auxiliary information. Its major idea is to use auxiliary information to structure calibration weights, attaching them to survey data, in order to improve the accuracy of the gross or mean estimation. Calibration estimation problem with box constraints is equivalently to solve a nonlinear equations system. Mnnich at...

Variational inequalities, nonlinear programming, complementarity problems and other problems can be reduced to nonsmooth equations, for which some generalizations of Newton's method are known. The Newton path, as a natural generalization of the Newton direction, was suggested by D. Ralph for enlarging the convergence region (globalization) of Newton-Robinson's method in the nonsmooth case. We i...

In this paper we describe a variant of the Inexact Newton method for solving nonlinear systems of equations. We define a nonmonotone Inexact Newton step and a nonmonotone backtracking strategy. For this nonmonotone Inexact Newton scheme we present the convergence theorems. Finally, we show how we can apply these strategies to Inexact Newton Interior–Point method and we present some numerical ex...