341. Derivative-Free Bilevel Optimization with Inexact Lower-Level Solutions
Invited abstract in session WC-1: Advances in Multiobjective and Bilevel Optimization without Derivatives, stream Zeroth and first-order optimization methods.
Wednesday, 14:00-16:00Room: B100/1001
Authors (first author is the speaker)
| 1. | Edoardo Cesaroni
|
| Department of Computer, Control, and Management Engineering Antonio Ruberti, Università di Roma "La Sapienza" | |
| 2. | Giampaolo Liuzzi
|
| DIAG, Sapienza Univ. of Rome | |
| 3. | Stefano Lucidi
|
| Department of Computer, Control, and Management Science, University of Rome "La Sapienza" |
Abstract
In this work, we introduce derivative-free frameworks for bilevel optimization. We consider both the upper and lower-level problems with bound constraints on the variables, as well as general nonlinear constraints, assuming that first-order information is not available or it is impractical to obtain. The lower-level problem is solved with an accuracy that is progressively refined throughout the optimization process.
Initially, we analyze the case where the upper-level problem is subject only to bound constraints, establishing convergence to Clarke-Jahn stationary points when the refinement process is allowed to reach its maximum precision. When a stricter limit is imposed on accuracy, we prove convergence to approximate stationary points using an extended notion of Goldstein stationarity.
Finally, we extend the proposed approach to handle more complex constraints via an exact penalty function approach, proving convergence to stationary points under suitable assumptions.
Keywords
- Derivative-free optimization
- Black-box optimization
- Multi-level optimization
Status: accepted
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