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arXiv · 1904.06231

Stability of the solution set of quasi-variational inequalities and optimal control

Amal Alphonse·Michael Hintermüller·Carlos N. Rautenberg
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Abstract

For a class of quasi-variational inequalities (QVIs) of obstacle-type the stability of its solution set and associated optimal control problems are considered. These optimal control problems are non-standard in the sense that they involve an objective with set-valued arguments. The approach to study the solution stability is based on perturbations of minimal and maximal elements of the solution set of the QVI with respect to {monotone} perturbations of the forcing term. It is shown that different assumptions are required for studying decreasing and increasing perturbations and that the optimization problem of interest is well-posed.

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Amal Alphonse, Michael Hintermüller, Carlos N. Rautenberg. 2019-04-12. Stability of the solution set of quasi-variational inequalities and optimal control. https://arxiv.org/abs/1904.06231

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