The Optimality Conditions For Vector Extremum Problems & The New Algorism For The General Quadratic Programming

In this thesis, some topics on vector optimization theory in abstract spaces are discussed, and a new algorithm for the general quadratic programming is studied as well. The concept of cone-subconvexlike map is defined in linear spaces and in linear topological spaces. The concept of (u, O?; Y+)-generalized convex is defined in linear spaces. The corresponded alternative theorems are proved with those generalized convexity conditions. And then, by applying the alternative theorems, the optimality conditions of two kinds of generalized convex extremum problems are given in linear spaces. The optimality conditions (with G-differential) and Lagrange duality theorems of non-constrained programming are presented in linear topological spaces. Finally, a new algorithm for quadratic programming with inequality constraints is offered The new method, by applying the dimension-descending algorithm with equality constraints, assures that every iterative element is feasible. It is shown that the algorithm is efficient being compared with the results of numerical tests and the accurate solutions. The whole program is designed with C++ language and runs passed on the microcomputer.