A combined homotopy method for nonconvex multi-objective programming problem with equality and inequality constrains

We solve a class of nonconvex multi-objective programming problem with equality and inequality constrains using the homotopy method. We develop a new shifted cone condition and generate the homotopy equation. Under that conditions, we prove that for almost every point in the feasible region, a smooth and bounded homotopy path can be derived and that the algorithm converges to the K-K-T point of multi-objective programming problem.