Data Processing with Combined Homotopy Methods for a Class of Nonconvex Optimization Problems

On the existing theoretical results, this paper studies the realization of combined homotopy methods on optimization problems in a specific class of nonconvex constrained region. Contraposing to this nonconvex constrained region, we give the structure method of the quasi-normal, prove that the chosen mappings on constrained grads are positive independent and the feasible region on SLM satisfies the quasi-normal cone condition. And we construct combined homotopy equation under the quasi-normal cone condition with numerical value and examples, and get a preferable result by data processing. The application of hometopy methods were used well in different areas(see details Allgower, Georg[1]), in mathematical programming, Garcia, Zangwill[2] used homotopy method firstly to study solving convex programming and got extensive convergence theorem[3-5]. And studying on solving convex programming and nonconvex programming problem by means of combined hometopy interior point method under weak condition through data processing. we got several interested results.