混合整数二次规划的全局充分性最优条件

Sufficient Global Optimality Conditions for Mixed-Integer Quadratic Minimization Problem with Inequality Constraints

利用一些学者提出的一种研究全局最优化问题的全局最优性条件的新方法,讨论了一些带有二次约束的非凸二次规划问题的全局最优性条件。本文主要通过利用拉格朗日函数F(λ,u)=1/2xTH_(λ,u)x+b_(T,u)λx+sum from i=i∈I(λici)+sum from j=j∈Jμjcj,正则锥(NL,D(x0)={l∈L:l(y)-l(x0)≤0,y∈D})和L-次微分相结合的方法,给出了带不等式约束的混合整数二次规划最小问题的全局极小点的全局最优性充分条件,而且推广了现有文献中的一些结论。同时通过一些实值例子说明了本文给出的最优性充分条件的可行性和有效性。

In this paper,we mainly study the global optimality conditions for some noncovex quadratic problems with quadratic constraints by using an approach to establish sufficient global conditions suggested by Z.Y.Wu.In this paper,we give global optimality conditions of global minimizer point for mixed integer quadratic minimizer programming with inequality and equality constrains by using lagrangian function F（λ,u）=1/2xTH（λ,u）x＋bTλ,ux＋∑i∈I（λici）＋∑j=j∈Jμjcj,normal cone （NL,D（x0）={l∈L：l（y）-l（x0）≤0,y∈D}） and L-subdifferential approach .Firstly ,we proof lemma 1 and proposition 2 .Then by using above two conclusions,some sufficient global optimality conditions for mixed-integer quadratic minimization problem with inequality are obtained.Based on the theorem,we get several deductions.Lastly,the effective and feasibility of sufficient optimality conditions are illustrsted by some numerical examples.