Semi-Infinite Mulitiobjective Programming With γ-Invex Fnctions

Semi-infinite Programming (SIP) and Multiobjective Programming (MP), asimportant parts of mathematical programming, have wide applications in many fieldssuch as engineering design, optimal control, economic equilibrium, managementscience and information technology. In this thesis, some topics on the semi-infinitemultiobjective problems are discussed.First, this paper recalls the definitions and research status of convexity andgeneralized convexity, and the origin, meaning and research status of multiobjectiveprogramming and semi-infinite programming. Based on the Fritz-John necessarycondition, we established the Karush-Kuhn-Tucker necessary condition andKarush-Kuhn-Tucker sufficient condition for Semi-Infinite MulitiobjectiveProgramming (SIMP), which the objective function and constraint function aredifferentiable involving γ-invex functions. At the same time, Mond-Weir duality andmixed duality model of semi-infinite mulitiobjective programming are established,including weak duality theorem, strong duality theorem and inverse duality theorem.