Research On A Class Of Generalized Quasi-Differentiable Functions And Solve The KKT Condition For Two-Level Programming

This thesis studies the KKT condition for a class of two-level programming. The theories of generalized quasi-differentiable functions (the extension of Farkas lemma) and the conclusions of semi-infinite programming are used to transform a class of two-level optimization programming to generalized quasi-differentiable optimization programming, and educe the KKT condition. Then the KKT condition for the more general two-level programming of this class also is educed.In Chapter 1, the space of families of pair of convex sets is introduced, which is the quotient space of the set of families of convex sets under suitable equivalence relations. Also part of the differential theories of a class of generalized quasi-differentiable functions, which based on the theory of the space of families of convex sets, is introduced. In the differential theory, firstly, the definition of generalized quasi-differentiable is introduced, then the differential calculus of pointwise maximum and pointwise minimum functions which are refered to are the key parts.In Chapter 2, the optimality conditions for generalized quasi-differentiable optimization problems. In the optimality conditions, besides necessary conditions and sufficient conditions for unconstrained optimizations and a necessary condition for constrained optimizations are introduced, the extension of weaken Farkas lemma and the extension of Farkas lemma are introduced as the key, which are the theoretical basic for the development of the KKT condition of the two-level programming.In Chapter 3, the conclusions of semi-infinite programming are introduced. Use these conclusions and under more strict conditions, we can transform a class of two-level programming into a class of generalized quasi-differentiable functions programming, and use the extension of Farkas lemma to educe the KKT condition. And we also can educe the KKT condition for the more general two-level programming of this class. By these, the theories of generalized quasi-differentiable have been enriched.