Homotopy method for solving mathematical programs with bounded box-constrained variational inequalities
Chunyang Zhang, Zhichuan Zhu, Yonghong Yao, Qinghuai Liu · Optimization · 2019
On the basis of Robinson's normal equation and smoothing projection operator, a homotopy method for solving mathematical programs with box-constrained variational inequalities (MPBVI) is presented. In which, the Chen–Harker–Kanzow–Smale smooth function is used to transform MPBVI into a smooth optimization problem. Under some mild assumptions, the existence and global convergence of a smooth path from almost any initial point to the GKKT point of the approximate problems is proven. And, the convergence of the GKKT point to a strong C-stationary point of the original problems is proved. Finally, some numerical results are given to show the effectiveness and feasibility of the homotopy method.