Abstract: We solved a semi-interior point combined homotopy equation for variational Inequality problems with inequality and inequality constraints. Under weak conditions, we proved the existence, boundedness and convergence of homotopy paths starting from any point in Rⁿ, and verified the feasibility and effectiveness of the semi-interior point combined homotopy method for solving variational inequality problems with equality and inequality constraints by using numerical examples.

Key words: non-interior homotopy method, variational inequality, global convergence