The Construction Methods Of The Dynamic Constraint Function And Its Application In Nonconvex Optimization Problems

A constraint shifting combined homotopy(CSCH)method for solving non-convex programming problems is an effective method.For the proposed method,the starting point needs to be only in the shifted feasible set not necessarily in the original feasible set,and the normal cone condition need only be satisfied in the boundary of the shifted feasible set not the original constraint set.It is different from the "quasi-normal cone condition" and "pseudo-cone condition" that Compared with the modified combined homotopy interior point method for solving non-convex programming problems,the construction of homotopy mapping is easier,the given conditions are weaker,and the application is more convenient.This paper constructs the constraint function based on a specific type of non-convex programming problem in the non-convex domain,and gives the concrete construction method of the dynamic constraint function,by adding parameters to the original constraint function,the original constraint function can be transformed into a function with parameter variable,which can satisfy the change of parameter t.The feasible region composed of the parameter variable constraint function can be continuously deformed the original nonconvex feasible region from the convex feasible region.First,this paper give the multi-pointed non-convex domain and the star-shaped nonconvex domain of constructing the constraint shifting function.It is different that constructing the star-shaped non-convex domain constraint shifting function in the process.Secondly,We prove that dynamic constraint function satisfies the boundary regularity condition and the normal cone condition under weaker conditions.Finally,Numerical examples show that the construction method is feasible and effective.construct the constraint function...