A Set Segmentation Method For A Class Of Optimization Problems In Nonconvex Set

In this paper,the feasible set of a class of nonconvex optimization problems is studied and the nonconvex optimization problems in nonconvex set with holes is studied mainly.Reference for the combined homotopy method,the set segmentation methodfor a class of optimization problems innonconvex set is given.First,segment the nonconvex set with holes into sets that satisfy the normal cone condition respectively.Thus,the original problem is divided into relatively independent subproblems with the feasible sets satisfy the normal cone condition respectively.Then,the relationship between the K-K-T point of the subproblems and the K-K-T point of original problem is proved.Thus,obtain the K-K-T point of original problem.The set segmentation method extends the application of the combined homotopy method.