THE INEXACT LOG-EXPONENTIAL REGULARIZATION METHOD FOR MATHEMATICAL PROGRAMS WITH VERTICAL COMPLEMENTARITY CONSTRAINTS

We study the convergence of the log-exponential regularization method for mathematical programs with vertical complementarity constraints (MPVCC). The previous paper assume that the sequence of Lagrange multipliers are bounded and it can be found by software. However, the KKT points can not be computed via Matlab subroutines exactly in many cases. We note that it is realistic to compute inexact KKT points from a numerical point of view. We prove that, under the MPVCC-MFCQ assumption, the accumulation point of the inexact KKT points is Clarke (C-) stationary point. The idea of inexact KKT conditions can be used to define stopping criteria for many practical algorithms. Furthermore, we introduce a feasible strategy that guarantees inexact KKT conditions and provide some numerical examples to certify the reliability of the approach. It means that we can apply the inexact regularization method to solve MPVCC and show the advantages of the improvement.