摘要
探讨带有变分不等式约束的优化问题的约束系统的稳定性与可行域法锥表达式之间的联系,尤其研究不同解映射的稳定性对正则法锥和极限法锥表达式的影响.研究表明解映射的平稳性可以保证正则法锥的上包含形式的表达式,且在一定约束规范下保证极限法锥的上包含形式的表达式;广义解映射的平稳性可直接保证极限法锥的上包含形式的表达式,且在一些集合正则条件下保证极限法锥的等式形式的表达式.上述结果为进一步研究带有变分不等式约束的优化问题的最优性条件奠定基础.
We discuss the relationship between stability of constrained system of optimization problem with variational inequality constraints and the expression of normal cone on feasible set,especially study the effect of different stability concept on the expression of regular normal cone and limiting normal cone.The study shows that the calmness of the solution mapping can ensure the upper inclusion expression of regular normal cone,and ensure the upper inclusion expression of limiting normal cone under some constraint qualification.The calmness of the generalized solution maps can directly ensure the upper inclusion expression of limiting normal cone,and ensure the equality type expression of limiting normal cone under some set regularity conditions.The above results lay the foundation for further research on the optimality conditions of the optimization problem with variational inequality constraints.
出处
《辽宁师范大学学报（自然科学版）》
CAS
2016年第3期305-310,共6页
Journal of Liaoning Normal University:Natural Science Edition
基金
国家自然科学基金资助项目(11201210
11671183)
关键词
带有变分不等式约束的优化问题
稳定性
法锥
正则法锥
optimization problem with variational inequality constraints
stability
normal cone
regular normal cone
