全局优化方法广泛应用于工程设计、金融管理、生物工程和社会科学等领域，已成为优化领域中非常重要的研究方向。由于问题本身存在多个不同的局部极小点，在求解过程中面临两个困难：如何跳出当前局部极小点得到目标函数值更小的局部极小点和如何判别当前的极小点是否是全局极小点，因此无法直接用传统的非线性规划方法来求解全局优化问题。本项目充分利用申请者在该领域所取得的前期研究成果，将抽象次微分法、下估计函数和择一性定理结合起来研究一些带有线性不等式约束非凸二次规划问题的一些全局最优性条件，例如箱子约束非凸二次规划问题、线性不等式约束非凸二次规划问题以及线性不等式约束混合整数二次规划问题等，并利用获得的新的全局最优性条件设计出具有良好终止准则的全局最优化方法。

Frequently, practitioners need to solve global optimization problems in many fields such as engineering design, financial management, bioengineering and social science. However, due to the existence of multiple local minimizers that differ from the global solution, we have to face two difficulties: how to jump from a local minimizer to a smaller one and how to judge that the current minimizer is a global solution. Hence all these problems cannot be solved by classical nonlinear programming techniques directly. The project makes full use of the applicant’s previous research results obtained in this field. The aim of this project is to develop some verifiable global optimality conditions for some nonconvex quadratic programs，such as nonconvex quadratic programming problems with box constraints，quadratic minimization problem under linear inequality and box constraints and mixed integer quadratic programming problems with linear inequality constraints, and to present some global optimization methods possessing nice stopping criteria by using the obtained global optimality conditions.