413. Approximation and exact penalization in simple bilevel variational problems
Invited abstract in session MD-7: Methods for simple and nonsmooth bilevel optimization, stream Bilevel and multilevel optimization.
Monday, 16:30-18:30Room: B100/5015
Authors (first author is the speaker)
| 1. | Riccardo Tomassini
|
| Computer, Control and Management Engineering Antonio Ruberti, Sapienza University of Rome | |
| 2. | Giancarlo Bigi
|
| Dipartimento di Informatica, Universita' di Pisa |
Abstract
In this talk we analyse a simple bilevel problem, where the lower-level is a monotone variational inequality and the upper-level is a convex optimization problem. Regularity is gained by adding a given degree of inexactness to the lower-problem and allows us to leverage techniques of exact penalization, bounding the growth of the penalization parameter. The resulting
penalized problem relies on the reformulation of the lower-level through the Minty gap function, that we approximate with cutting planes techniques. We devise different algorithms to treat the affine and non-affine cases, we discuss their convergence and provide theoretical bounds on the final degree of inexactness. Numerical results are reported for the non-affine case to test the sensitivity of the problem to several parameters, showing that the true final inexactness is generally meaningfully lower than the theoretical one.
Keywords
- Multi-level optimization
- Complementarity and variational problems
- Non-smooth optimization
Status: accepted
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