Non-convex Optimization Cohesion Dynamic Constraints Combined Homotopy Algorithm

Optimization problem refers to there are many feasible solutions to a given problem.Among these solutions,we can choose the best one that we considered in a certain way.The combined homotopy method solved a lot of optimization problems,compared with other algorithms it has unique advantages on solving the optimization problem.At the same time,in order to study the Unitary computation approach of Nonconvex programming,in 1993,the Combined Homotopy Interior Point Method(CHIP) was proposed by Feng guochen,Yu bo and Lin zhenghua, which using Newton-homotopy and Fixed Point-Homotopy Method for solving Nonconvex programming,on the condition that the feasible region to meet normal cone condition,that is,when the normal cone of feasible region does not contain the points in the feasible region to proved that the algorithm converges to the Kuhn-Tucke Point.As for the situation of the feasible region is not smooth,it also proved that the global convergence of the above mentioned method,by using the technique of Aggregate Function. As we all known, normal cone condition is a restraction of nonconvex set,and is also the necessary boundary condition which to ensure Homotopic mapping posses accessibility,weaking these conditions will be expanded scope of application of algorithm.Recently, there are many reserchers study on The combined homotopy method of the optimization problem in nonconvex set,in this paper,Chapter 1-4 studied the combined homotopy method of Nonconvex programming and nonlinear programming,chapter 8 and chapter 12 studied the combined homotopy method of the optimization problem that meet the requirements of normal cone condition and pseudo-normal cone condition.In chapter5,10,11 disscussed the combined homotopy method which solved variational inequality, chapter 9 is mainly analyses combined homotopy method of Nonconvex programming and nonlinear programming which on unbounded domain,In chapter 6 and chapter 7 analyses combined homotopy method that by using the aggregate function to construct combined homotopy equation,which solved the optimization problem.Chapter 13 constructed dynamic constraint Function and Homotopy equation,which solved the problem of combined homotopy method of convex programming,Nonconvex programming and nonlinear programming.In this paper,with supporting theory of homotopy method, Aggregate Function, Differential geometry, nonsmooth,analysis topology, analyses dynamic constraint function and Aggregate dynamic constraint function that constructed by several kinds of functions. At the first, construct Aggregate dynamic constraint function which is close to boundary function,then use the Aggregate dynamic constraint function to construct combined homotopy function,thus,provide the K-K-T point of the above optimization problem. Finally, provide Computer Program which is solved by the K-K-T point of the above optimization problem.At last,we made a agglomeration Dynamic constraint function,and when the Original Boundary satisfy the independent Conditions we prove the agglomeration Dynamic constraint Boundary also satisfy the independent conditions in a small range.Made the Homotopy equation of the agglomeration Dynamic constraint Boundary.And then also prove the Existence and Boundedness of Homotopy path.