60. Directional combined approach for bilevel programs
Invited abstract in session WB-7: Theory and methods for bilevel optimization, stream Bilevel and multilevel optimization.
Wednesday, 10:30-12:30Room: B100/5015
Authors (first author is the speaker)
| 1. | Kuang Bai
|
Abstract
In this paper, by employing the combined approach, we reformulate the bilevel programs into an equivalent set-constrained single-level problem, which however is nonsmooth. We introduce the directional partial calmness condition to penalize nonsmooth constraints into the objective function, then derive the directional necessary optimality condition under the directional metric subregularity/quasi-normality conditions. The directional partial calmness condition is generally weaker than the nondirectional one and thus more likely to hold. Furthermore, we establish sufficient conditions for directional partial calmness. An example is provided to illustrate that the directional partial calmness condition is satisfied for the bilevel programs, whereas the nondirectional condition does not hold, thereby validating the sufficiency of the conditions we have presented.
Keywords
- Multi-level optimization
Status: accepted
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