A regularized smoothing Newton method for symmetric cone complementarity problems

This paper extends the regularized smoothing Newton method in vector complementarity problems to symmetric cone complementarity problems (SCCP), which includes the nonlinear complementarity problem, the second-order cone complementarity problem, and the semidefinite complementarity problem as special cases. In particular, we study strong semismoothness and Jacobian nonsingularity of the total natural residual function for SCCP. We also derive the uniform approximation property and the Jacobian consistency of the Chen–Mangasarian smoothing function of the natural residual. Based on these properties, global and quadratical convergence of the proposed algorithm is established

Solvability of Newton equations in smoothing-type algorithms for the SOCCP

AbstractIn this paper, we first investigate the invertibility of a class of matrices. Based on the obtained results, we then discuss the solvability of Newton equations appearing in the smoothing-type algorithm for solving the second-order cone complementarity problem (SOCCP). A condition ensuring the solvability of such a system of Newton equations is given. In addition, our results also show that the assumption that the Jacobian matrix of the function involved in the SOCCP is a P0-matrix is not enough for ensuring the solvability of such a system of Newton equations, which is different from the one of smoothing-type algorithms for solving many traditional optimization problems in ℜn

Numerical Analysis of Algorithms for Infinitesimal Associated and Non-Associated Elasto-Plasticity

The thesis studies nonlinear solution algorithms for problems in infinitesimal elastoplasticity and their numerical realization within a parallel computing framework. New algorithms like Active Set and Augmented Lagrangian methods are proposed and analyzed within a semismooth Newton setting. The analysis is often carried out in function space which results in stable algorithms. Large scale computer experiments demonstrate the efficiency of the new algorithms