Optimization Seminar: Dr. Xiaoni Chi

Title: The Jacobian consistency of a smoothed generalized Fischer-Burmeister function for the second-order cone complementarity problem

Second-order cone (SOC) complementarity functions and their smoothing functions play an important role in the solution of the second-order cone complementarity problem. In this talk, we propose a smoothing function of the generalized Fischer-Burmeister function, which is also called the smoothed generalized Fischer-Burmeister function, and show its Jacobian consistency. Moreover, we estimate the distance between the subgradient of the generalized Fischer-Burmeister function and the gradient of its smoothing function. These results will play an important role for achieving the rapid convergence of smoothing methods.