Optimality Conditions And Approximation Algorithm Of Nonsmooth Optimization Problems

The research of nonsmooth optimization problems in theory and algorithm occupies an important place in mathematical programming and arises in application of engineering and production management and construction of national defence, etc. At the same time, any research of minimizing smooth problem is closed linked with extent of nonsmoothness. Quasidifferentiable functions are a class of important nonsmooth funtions including differentiable functions, convex functions, concave functions and their composite functions in a more general sense. In this thesis, based on a class of minimizing indifferentiable optimization problem, using the properties of convex compact set, corresponding optimality conditions under distint circumstances are obtained by the means of quasidifferentiable notion and results in the Demyanov sense. Futhermore, the problem above is generalized to the nomal form of minimizing indifferentiable optimization problem and its mutiplicate optimality conditions are gived, convergence is proved based on the principles ofε?steepest descent. The research of these problems has not been vended in the publication by now and the conclusions are not only brief and practicable but also the generation involving optimality conditions of Fritz John. Finally, some conclusions are drawn about optimality conditions for inequality constrained quasidifferntiable multiobjective programming by using the properties of quasidifferentiable functions and the alternative theorem.