The Optimality Conditions And Duality Theory For Vector Extremum Problem Under (F,a,p,d) -Convexity & An Algorithm For Nonlinear Multi-objective Programming

In this thesis,the optimality sufficiency conditions and duality theory are discussed in multiobjective nonlinear programming involving (F, a,p ,d)-convexity and generalized (F, a, p ,d)-convexity. At that time,an algorithm is discussed for nonlinear multiobjective problem. Firstly,on the basis of (F, a, p ,d)-convexity concept, concept of generalized (F,a, p ,d)- convexity is defined, the optimality sufficiency conditions are obtained under generalized (F, a, p ,d)-convexity assumptions for a multiobjective nonlinear program which involved inequality and equality. Secondly,the Wolfe vector duality and Mond-Weir vector duality are established under (F, a, p ,d)-convexity assumptions for a multiobjective nonlinear program which involved inequality and equality, weak daulity and strong duality theorems are proofed. furthermore,a mixed type dual for the primal problem is established and duality results are obtained.After that, the optimality sufficiency conditions and duality results for the nonlinear fractional programming problem are presented under generalized (F, or, p ,d)-convexity assumptions. Finally, an algorithm for nonlinear multiobjective programming with linear equality constraints is offered. At first, multiobjective programming is transformed into a single-objective programming by using linear qualitied method; and then, a single-objective programming with equality constraints is transformed into a series of linear equation systems, an algorithm is obtained by applying the dimension-descending algorithm with equality constraints. It is shown that the algorithm is efficient being compared with the results of numberical tests and the results of other methods. The whole algorithm is designed with C++ language and runs passed on the microcomputer.