The Duality Framework For Constrained Optimization Problems

The duality theory in constrained optimization problems are mainly discussed in this paper.For a nonempty subset in R n+1, two simple optimization problems are constructed.The necessary and sufficient conditions for the attainments and equality of the optimal values in duality theorems. They are the minimum and maximum theoremⅠ,ⅡThese problems will be used as an analytical framework for constrained optimization duality.Corresponds to the classical optimization problem, by means of the epigraph of the objective function,the original problem and its dual problem, as the minimax problems of a set, the strong duality theoremis obtained. And has applied the saddle points and perturbation functions related theorem and define got some conclusion Finally, a class of constrained optimization problems in Hilbert space are characterized,and it can be solved by dealing with its dual problem.