Global optimality conditions for nonlinear optimization problems

Based on the alternative theorem, global optimality conditions for nonlinear programming problems to be discussed in this article. Firstly, on the basis of the research of optimality conditions for polynomial optimization problems, the paper considers nonlinear programming over constrains which are not real polynomial functions. And then necessary global optimality conditions for nonlinear programming problems with non-polynomial constraints functions are proposed and sufficient global optimality conditions for polynomial objective function programming problems with non-polynomial constraints functions are developed by using the alternative theorem. Finally, necessary and sufficient global optimality conditions for 0–1 quadratic programming problems are presented.