Research On Some Problems In Bilevel Programming

The hierarchical system is the main form of the society activity, multilevel programming problem is developed to solve decentralized planning problem with multiple decision makers in this hierarchical system. Because of the outstanding realistic background and the extensive application prospects, it draws much attention and becomes a newly research domain. Some problems in bilevel programming are mainly studied in this thesis. Details are as follows:We deal with properties of bilevel linear programming and prove the equivalence of bilevel linear programming and optimization over the efficient set. A class of Multi-objective tow level programming, i.e. the upper-level is single objective and the lower-level is linear multi-objective, is mainly discussed. It can be converted into the optimization over the efficient set with parameter and an algorithm is given with its finite termination being proved; when the upper- level is linear function, an exact penalty function algorithm is given. As for price control problem, some properties of its feasible set are summarized; the price control problem with non-unique lower-level solutions is studied and an expected return model is given, which is beneficial to the investigations on practical problems.The module conversion for a kind of Max-min problems is given, namely, the Max-min problem with equality and inequality constraint is converted into convex problem with linear constraint, which provides theoretical basis for designing effective algorithms.