A study of one-parameter regularization methods for mathematical programs with vanishing constraints

Asymptotic regularity for Lipschitzian nonlinear optimization problems with applications to complementarity-constrained and bilevel programming

“…However, as we will see in Section 4, our results recover recently introduced notions of asymptotic stationarity and regularity for so-called mathematical programs with complementarity constraints (MPCCs for short), see Luo et al (1996); Outrata et al (1998), which have been shown to be useful in numerical practice, see Andreani et al (2019b); Ramos (2021). We note that our model program (P) covers other prominent classes from disjunctive programming like so-called or-and vanishing-constrained programs, see Achtziger and Kanzow (2008); Hoheisel and Kanzow (2007); Hoheisel et al (2020); Mehlitz (2020a,c) and Remark 4.3, so that our findings are likely to possess reasonable extensions to these models as well.…”

“…a so-called vanishing-constrained optimization problem is obtained, see e.g. Achtziger and Kanzow (2008); Hoheisel and Kanzow (2007); Hoheisel et al (2020) and the references therein for an overview. Introducing the Lipschitz continuous function ϕ vc : R 2 → R by means of…”