Number Of Vectors To Optimize The Nature Of The Problem Solution

This thesis mainly investigates two contents: One is the structure, the topological properties and the stability of the assessment functional solutions in the realm of the multi-objective optimization problem and the other the stability and the part stability of the (weak) efficient solutions in the realm of set-valued maps optimization problem. The stabilities of these solutions are all the generic stabilities obtained by using the mothod of usco. Based on it, the great majority of the optimization problems have more than one essential solution in the sense of Baire dimension. In other words, the solutions of the great majority of the optimization problems are low semi-continuous or almost low semi-continuous.Hence the present study sets out to explore the issues within the following proposed framework:It consists of two chapters. In chapter one, first of all, the present researcher reviews the minimal model of the multi-objective optimization problem: V-min/(x) in which f : X â†' E refers to a vector-valued function and Estands for a vector space. Secondly, by assessing the multi-objects, the paper turns the minimal problem of the multi-objective optimization into the minimal problem of the unique objective optimization: minh(f(x)), where h :Eâ†'R is a realfunction. Based on the new notions above, the present researcher succeeds in obtaining the generic stability, structure and topological properties of the assessment functional solutions.In chapter two, based on the relevant theories of the set-valued maps optimization problems, firstly, the paper researches the generic stability of the weak efficient solutions in the premises of consistent topology case and the graph topology case. Secondly, the paper achieves the part u.s.c. property of efficient solution based on the consistent topology case. Finally, using set-value maps, the paper concludes our considerations on the ideal solutions.