论文标题
方向性必要的最佳条件
Directional necessary optimality conditions for bilevel programs
论文作者
论文摘要
双光线程序是一个优化问题，其中约束涉及参数优化问题的解决方案。众所周知，价值函数重新重新制定提供了同等的单级优化问题，但它导致了一个非平滑的优化问题，该问题永远无法满足通常的约束资格，例如Mangasarian-Fromovitz约束资格（MFCQ）。在本文中，我们表明，即使是一阶的度量次频率的足够条件（通常比MFCQ弱）在二聚体程序的每个可行点上都失败了。我们介绍了定向平静条件的概念，并表明在{}方向镇静条件下，定向必要的最佳条件成立。 {虽然方向性最佳条件通常比非方向性条件更加明显，但}方向平静条件通常比经典的平静条件弱，因此更有可能保持。 {我们对值函数进行定向灵敏度分析，并提出定向准正常，作为方向平静的足够条件。给出了一个示例，以表明双杆计划的定向准正态条件可能存在。
The bilevel program is an optimization problem where the constraint involves solutions to a parametric optimization problem. It is well-known that the value function reformulation provides an equivalent single-level optimization problem but it results in a nonsmooth optimization problem which never satisfies the usual constraint qualification such as the Mangasarian-Fromovitz constraint qualification (MFCQ). In this paper we show that even the first order sufficient condition for metric subregularity (which is in general weaker than MFCQ) fails at each feasible point of the bilevel program. We introduce the concept of directional calmness condition and show that under {the} directional calmness condition, the directional necessary optimality condition holds. {While the directional optimality condition is in general sharper than the non-directional one,} the directional calmness condition is in general weaker than the classical calmness condition and hence is more likely to hold. {We perform the directional sensitivity analysis of the value function and} propose the directional quasi-normality as a sufficient condition for the directional calmness. An example is given to show that the directional quasi-normality condition may hold for the bilevel program.
