一类特殊六次规划问题的全局最优充分条件

Global Sufficient Optimality Conditions for a Special Class of Sixth Programming Problems

全局最优性条件是判断一个解是否为全局最优解的基本条件,在此前,已经有文献提出了非凸二次规划问题和非凸三次次规划问题的充分全局最优性条件,但是均未对六次规划问题进行研究.因此,本文利用L-次梯度方法,得到了带有箱子约束的非凸六次规划问题的全局最优充分性条件.此外,通过构造一类特殊的对角矩阵,以方便验证所提出问题的全局充分性条件.

The global optimality condition is the basic condition for judging whether a solution is a global optimal solution.Previously,some literature have proposed sufficient global optimality conditions for non-convex quadratic programming problem and non-convex cubic programming problem.The non-convex six-order programming problem were not studied.Therefore,the global optimal sufficiency condition of the non-convex six-order programming problem with box constraints is obtained by the L-subgradient method.In addition,a special diagonal matrix is constructed,which is used to provide a convenient method for justifying the proposed sufficient conditions.