Abstract: This paper deals with the combined homotopy methods for optimization problems on the partial reverse convex constraints feasible set. Contraposing to this partial reverse convex constrained domain, we gave the structure method of the quasinormal, proved that the chosen mappings are positive independent with respect to constrained grades. And the constrained quasinormal cone satisfies the quasinormal cone condition.

Key words: nonconvex feasible fields, combined homotopy interior point method (CHIP), quasinormal cone condition, partial reverse convex constraint, nonconvex optimization problem