Abs-Normal NLP与MPCC之间的关系。第二部分：弱约束规范
Relations between Abs-Normal NLPs and MPCCs. Part 2: Weak Constraint Qualifications
AI总结：
本文研究abs-normal形式非光滑NLPs与MPCCs的关系，引入Abadie和Guignard kink规范，证明与MPCC-ACQ/GCQ的联系，并定义M-和B-平稳性及一阶最优性条件。
摘要：
本工作继续开展一项持续的努力，旨在比较abs-normal形式的非光滑优化问题与具有互补约束的数学规划（MPCCs）。我们研究具有等式和不等式约束的abs-normal形式的一般非线性规划，即所谓的Abs-Normal NLP，及其与等价MPCC重构的关系。我们引入了Abadie和Guignard的kink规范的概念，并证明了对于对应的MPCC公式，这些概念与MPCC-ACQ和MPCC-GCQ之间的关系。由于[10]中提出的特定松弛重构的非唯一性，这些关系是非平凡的。结果表明，Abadie类型的约束规范得以保留。我们还证明了较弱的结果，即对于所有分支问题，Guignard（和Abadie）约束规范的等价性成立，而GCQ的保持问题仍然悬而未决。最后，我们为abs-normal NLP引入了M-平稳性和B-平稳性概念，并证明了与MPCC对应公式相对应的一阶最优性条件。
英文摘要：
This work continues an ongoing effort to compare non-smooth optimization problems in abs-normal form to Mathematical Programs with Complementarity Constraints (MPCCs). We study general Nonlinear Programs with equality and inequality constraints in abs-normal form, so-called Abs-Normal NLPs, and their relation to equivalent MPCC reformulations. We introduce the concepts of Abadie's and Guignard's kink qualification and prove relations to MPCC-ACQ and MPCC-GCQ for the counterpart MPCC formulations. Due to non-uniqueness of a specific slack reformulation suggested in [10], the relations are non-trivial. It turns out that constraint qualifications of Abadie type are preserved. We also prove the weaker result that equivalence of Guginard's (and Abadie's) constraint qualifications for all branch problems hold, while the question of GCQ preservation remains open. Finally, we introduce M-stationarity and B-stationarity concepts for abs-normal NLPs and prove first order optimality conditions corresponding to MPCC counterpart formulations.
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