The Optimality Conditions For Vector Extremum Problems & A Algorithm For Quadratic Programming With Linear Inequlities Constraints

In this thesis, some topics on vector optimization theory in abstract spaces are discussed, and a algorithm for quadratic programming problem with linear inequalities constraints is studied as well. In Banach space, the optimal concept of Contingent Cone is defined, and then, a generalized constrained qualification is given, thereafter, the optimal conditions of the differentiable optimization problem are obtained in Banach space; In linear toplogical space, a important property of (weak)efficient points of set is given , and then, the sufficient and the neccessory conditions of the vector extremum problem with constraint are obtained; Finally, this thesis gives a algorithm for quadratic programming problem with linear inequalities constraints, and its convergence is analysized in some degree, moreover, this algorithm is efficient compared with the results of numerical tests...