44. On the weakest constraint qualification for sharp local minimizers
Invited abstract in session TB-3: In memory of Georg Still - part 1, stream In memory of Georg Still.
Thursday, 10:05 - 11:20Room: M:J
Authors (first author is the speaker)
| 1. | Oliver Stein
|
| Institute of Operations Research, Karlsruhe Institute of Technology | |
| 2. | Maximilian Volk
|
| Institute of Operations Research, Karlsruhe Institute of Technology |
Abstract
A result of Georg Still and Martin Streng characterizes the sharp local minimality of feasible points of nonlinear optimization problems by a strengthened version of the Karush–Kuhn–Tucker conditions, as long as the Mangasarian–Fromovitz constraint qualification holds. This strengthened condition is not easy to check algorithmically since it involves the topological interior of some set. In this article, we derive an algorithmically tractable version of this condition, called strong Karush–Kuhn–Tucker condition. We show that the Guignard constraint qualification is the weakest condition under which a feasible point is a strong Karush–Kuhn–Tucker point for every continuously differentiable objective function possessing the point as a sharp local minimizer. As an application, our results yield an algebraic characterization of strict local minimizers of linear programs with cardinality constraints.
Keywords
- Linear and nonlinear optimization
Status: accepted
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