398. On the relation between approximate and exact stationarity in disjunctive optimization
Invited abstract in session WB-6: Structured nonsmooth optimization -- Part II, stream Nonsmooth and nonconvex optimization.
Wednesday, 10:30-12:30Room: B100/7013
Authors (first author is the speaker)
| 1. | Isabella Käming
|
| Technische Universität Dresden | |
| 2. | Patrick Mehlitz
|
| Philipps-Universität Marburg |
Abstract
We consider approximate stationarity conditions, constraint qualifications, and qualification conditions for optimization problems with disjunctive constraints, i.e., geometrically constrained problems with a constraint set that can be written as a union of convex polyhedral sets. This class of optimization problems covers, among others, optimization problems with complementarity, vanishing, switching, or cardinality constraints. In this talk, we first investigate suitable concepts of approximate stationarity and their connection to Mordukhovich- and, more importantly, even strong stationarity. The respective connections are established using strict constraint qualifications, particularly, so-called approximate regularity conditions. As an alternative approach to using strict constraint qualifications, we then introduce a new qualification condition which, based on an approximately stationary point, can again be used to infer its Mordukhovich- or strong stationarity. In contrast to the approximate regularity conditions, this condition depends on the involved sequences justifying approximate stationarity and, thus, is not a constraint qualification in the narrower sense. However, we will see that the new condition offers the benefits of being strictly weaker and much easier to verify than the strict constraint qualifications.
Keywords
- Complementarity and variational problems
- Linear and nonlinear optimization
Status: accepted
Back to the list of papers