The Combined Homotopy Method For Solving A Class of Programming Problems With A Bounded Feasible Set

摘要

In this paper, we study the following nonlinear nonconvex programming problem: {minf(x)/ε.t.g.(x)≤0,i∈M,M={1.2,...,M}. Under the condition that the feasible set is bounded and connected, but it has a point that the boundary is not regular at this point, we propose the combined homotopy method to solve this problem by constructing a new constraint function and a combined homotopy equation. The convergence of the method is proved and the existence of a smooth homotopy path from any interior point to a solution of the problem is established.Our method is very different from previous homotopy method. Numerical examples show that this method is feasible and effective.