非对称锥优化问题KKT函数的B次微分非奇异性与非退化性条件

B-subdifferential nonsingularity and constraint nondegeneracy of KKT function for the asymmetric cone optimization problem

针对非对称锥上的优化问题的局部最优解,主要讨论其灵敏性问题。计算了KKT函数的B次微分,给出了KKT函数的强二阶充分条件和非退化约束条件隐含的B次微分的非奇异点、KKT函数的B次微分非奇异点隐含的KKT点的强正则性和KKT函数的B次微分非奇异点隐含的非退化约束条件。得到了强二阶充分条件、非退化性约束、KKT函数的B次微分非奇异性与KKT点的强正则性之间的关系。

For the local optimal solution of an optimization problem on anasymmetric cone,this paper discusses the sensitivity properties of the local optimal solutions.In this paper,the B-subdifferential of the KKT function is calculated,and the nonsingular points of B-subdifferential implied by the strong second order sufficient condition and constraint nondegeneracy of KKT function,the strong regularity of B-subdifferential implied by KKT function and the constraint nondegeneracy implied by KKT function are given.Then the relationship among strong second order sufficient condition,constraint nondegeneracy,B-subdifferential nonsingularity of the KKT function and strong regularity of the KKT points is obtained.