A Nonmonotone Smoothing Algorithm for Second-Order Cone Programming in Failure Criteria

摘要

It is shown that a wide variety of material failure criteria can be represented as second-order cone problems. In this paper, we present a nonmonotone smoothing Newton algorithm for solving the second-order cone programming (SOCP) in material failure criteria. Based on a new Fischer-Burmeister smoothing function, our smoothing algorithm reformulates SOCP as a nonlinear system of equations and then applies Newton's method to the system. The proposed algorithm solves only one linear system of equations and performs only one nonmonotone line search at each iteration. It is shown that the algorithm is globally and locally quadratically convergent under suitable assumptions.