论文标题
ABS NLP和MPCC之间的关系。第2部分：较弱的约束资格
Relations between Abs-Normal NLPs and MPCCs. Part 2: Weak Constraint Qualifications
论文作者
论文摘要
这项工作继续进行持续的努力，将ABS-Normal形式的非平滑优化问题与具有互补性约束（MPCC）的数学程序进行比较。我们研究具有平等性和不平等限制的一般非线性计划，以ABS正常形式，所谓的ABS-NLPS及其与同等MPCC重新纠正的关系。我们介绍了Abadie's和Guignard的纠结资格的概念，并证明了与MPCC-ACQ和MPCC-GCQ的关系，以使用对应MPCC配方。由于[10]中建议的特定松弛重新印象的非唯一性，这种关系是不平凡的。事实证明，保留了Abadie类型的约束资格。我们还证明，对所有分支问题的限制资格的等效性较弱，而GCQ保存问题仍然开放。最后，我们为ABS NLP介绍了M-Stationarity和B-Stationarity概念，并证明了与MPCC对应物配方相对应的一阶最佳条件。
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.
