具有（F,α，ρ，θ）-b-凸的多目標(biāo)分式規(guī)劃的最優(yōu)性條件和對(duì)偶性.pdf

1、南昌航空大學(xué)碩士學(xué)位論文具有（F,α，ρ，θ）-b-凸的多目標(biāo)分式規(guī)劃的最優(yōu)性條件和對(duì)偶性姓名：李動(dòng)鋒申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：最優(yōu)化理論與算法指導(dǎo)教師：邱根勝20070601II ABSTRACT An important aspect for the theory research of the multi- objective optimization problems ( ) MOP is to find ou

2、t the optimality conditions for ( ) MOP under more generalized convexity hypothesizes, establish duality for original problems and explore the relation between the solutions of the original and the duality p

3、roblems. In recent years, many authors have been studying the multi- objective fractional programming problems ( ) MFP under the assumption of a variety of generalized convexity. Many optimality conditions

4、 and duality theorems of ( ) MFP have been given based on the concepts of a variety of generalized convexity. In this paper, we present a new formulation of generalized convex function-( , , ,

5、) F b α ρ θ ? ? convex function. Under the assumption of ( , , , ) F b α ρ θ ? ? convexity , ker Kuhn Tuc ? type optimality conditions and saddle- point type optimality conditions and Mond Weir ?duality, Lag

6、range duality, Schaible duality for ( ) MFP are discussed .The paper consists of 5 chapters. In chapter 1, we review the origins，the mathematics models，the research directions of( ) MOP and the rec

7、ent advances in the study of( ) MFP with generalized convexity. Then the works we have done on this problem are introduced. In chapter 2, we firstly review some basic concepts about the generalized con

8、vexity of function and present a new formulation of generalized convex function-( , , , ) F b α ρ θ ? ? convex function. Then several lemmas are presented. The chapter 3 and the following chapter

9、are the main part of the paper .In chapter 3, firstly, under the assumptions of ( , , , ) F b α ρ θ ? ? convexity, we present several ker Kuhn Tuc ?type optimality conditions in which the weak efficiency

10、and efficiency are involved .Then under the assumption of ( , , , ) F b α ρ θ ? ? convexity of the objective function and constraint functions, an equivalent multi- objective programming problem named ( ) ( , ,

11、 , ) ( ) F VP x α ρ θis constructed by a modification of the objective function of ( ) MFP . At the same time, the ( , , , ) F b Lagrange α ρ θ ? ?function and a new type of saddle points of ( ) ( , ,

12、, ) ( ) F VP x α ρ θare defined .At last, we present the Lagrange saddle- point type optimality conditions in which the efficiency are involved. In chapter 4, we firstly discuss three duality types which

13、 are Mond Weir ?type, Lagrange type and Schaible type, then the weak duality theorems and strong duality theorems are proved for the three types of duality respectively based on the ( , , , ) F b