Develops optimistic and pessimistic calculus rules for set-valued bilevel constraints, derives nonsmooth adjoint inclusions, and proposes a convergent single-loop algorithm demonstrated on total variation inverse problems.
A non-smooth trust-region method for locally Lipschitz functions with application to optimization problems constrained by variational inequalities
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abstract
We propose a nonsmooth trust-region method for solving optimization problems with locally Lipschitz continuous functions, with application to problems constrained by variational inequalities of the second kind. Under suitable assumptions on the model functions, convergence of the general algorithm to a C-stationary point is verified. For variational inequality constrained problems, we are able to properly characterize the Bouligand subdifferential of the reduced cost function and, based on that, we propose a computable trust-region model which fulfills the convergence hypotheses of the general algorithm. The article concludes with the experimental study of the main properties of the proposed method based on two different numerical instances.
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math.OC 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Single-loop approaches to nonsmooth bilevel optimisation
Develops optimistic and pessimistic calculus rules for set-valued bilevel constraints, derives nonsmooth adjoint inclusions, and proposes a convergent single-loop algorithm demonstrated on total variation inverse problems.