Global Optimality Conditions For Several Classes Of Programming Problems

Global optimization problems abound in economic modeling,finance,network andtransportation,database,chip-design,image processing,chemical engineering design and centrol,molecular biology and enviromental engineering.We pay more attention to some special classes of programming problems in the fields of local optimality problems and global optimality problems.So,it is very necessary to research some special classes of programming problems.In this thesis,we would study some global optimality conditions for the following classes of programming problems: mixed integer quadratic programming problems with inequality conditions, mixed integer quadratic programming problems with LMI conditions,multi-objective programming problems with polynomial constraints.In the first chapter of this thesis, we introduce the recent developments in global optimiza-tion. The sufficient global optimality conditions of mixed quadratic integer programming problems with inequality constraints are discussed in chapter 2. In chapter 3, some sufficient global optimality conditions for mixed quadratic integer programming problems with LMI constraints are established. In the forth chapter, we still study global optimality conditions of special programming problems, but in this section, the objective of programming problem is vector. What is more, we get some necessary global optimality conditions of multi-objective programming problems with polynomial constraints.Lastly,we also provide some numerical examples to illustrate our global optimality conditions.