A modified constraint shifting homotopy method for solving general nonlinear multiobjective programming

In this paper, for solving the general nonconvex multiobjective programming with both inequality and equality constraints, a modified constraint shifting homotopy is constructed, and the existence and global convergence of the smooth homotopy pathway is proven for any initial point in the almost Euclidean space under some mild conditions. The advantage of the newly proposed method requires that the initial point can be chosen much more conveniently, which needs to be only in the shifted feasible set not necessarily in the original feasible set. Meanwhile, the normal cone condition for proving the global convergence, which is much weaker than the existing interior method, need only be satisfied at the boundary of the shifted feasible set but not the original constraint set.