论文标题
非平滑优化问题的渐近平稳性和规律性
Asymptotic stationarity and regularity for nonsmooth optimization problems
论文作者
论文摘要
基于限制变异分析的工具，我们为非平滑数学程序提供了一个顺序必要的最佳条件，该条件可容纳没有任何其他假设。为了确保以这种新意义上的固定点已经是mordukhovich stationary，我们称之为“ AM-Regulace”的约束资格的存在是必要的。我们研究了来自非平滑优化的AM定型与其他约束资格之间的关系，例如基础可行性映射的度量（子）规律性。我们的发现应用于几何的优化问题，尤其是析取约束。这样，就表明AM-Recultions恢复了最近引入的锥形型型约束资格，有时从标准的非线性和互补性受限的优化中称为AKKT-Regullity。最后，我们讨论了AM-Regulacority在限制变异的演算中的一些后果。
Based on the tools of limiting variational analysis, we derive a sequential necessary optimality condition for nonsmooth mathematical programs which holds without any additional assumptions. In order to ensure that stationary points in this new sense are already Mordukhovich-stationary, the presence of a constraint qualification which we call AM-regularity is necessary. We investigate the relationship between AM-regularity and other constraint qualifications from nonsmooth optimization like metric (sub-)regularity of the underlying feasibility mapping. Our findings are applied to optimization problems with geometric and, particularly, disjunctive constraints. This way, it is shown that AM-regularity recovers recently introduced cone-continuity-type constraint qualifications, sometimes referred to as AKKT-regularity, from standard nonlinear and complementarity-constrained optimization. Finally, we discuss some consequences of AM-regularity for the limiting variational calculus.
