Recent trends and views on elliptic quasi-variational inequalities
Authors
- Alphonse, Amal
ORCID: 0000-0001-7616-3293 - Hintermüller, Michael
ORCID: 0000-0001-9471-2479 - Rautenberg, Carlos N.
ORCID: 0000-0001-9497-9296
2010 Mathematics Subject Classification
- 35J87 47J20 49K40 35J60
Keywords
- Quasi-variational inequalities, Mosco convergence, semismooth Newton methods
DOI
Abstract
We consider state-of-the-art methods, theoretical limitations, and open problems in elliptic Quasi-Variational Inequalities (QVIs). This involves the development of solution algorithms in function space, existence theory, and the study of optimization problems with QVI constraints. We address the range of applicability and theoretical limitations of fixed point and other popular solution algorithms, also based on the nature of the constraint, e.g., obstacle and gradient-type. For optimization problems with QVI constraints, we study novel formulations that capture the multivalued nature of the solution mapping to the QVI, and generalized differentiability concepts appropriate for such problems.
Appeared in
- Topics in Applied Analysis and Optimisation, M. Hintermüller, J.F. Rodrigues, eds., CIM Series in Mathematical Sciences, Springer Nature Switzerland AG, Cham, 2019, pp. 1--31.
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