The Constraint Shifting Combined Homotopy Method for Bounded General Programming Problems

摘要

In this paper, we study the nonlinear nonconvex with equality constraints and inequality constraints programming problems, under the condition that the feasible set is bounded and connected, and has a regular boundary, at first, we propose the constraint shifting combined homotopy method to solve this problem, by constructing constraint shifting functions and a combined homotopy equation. Then, the convergence of the method is proved and the existence of a smooth homotopy path from any interior point or infeasible interior point to the solution of the problem is established. At last, numerical examples show that this method is feasible and effective.