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Stability of the Solution Set of Quasi-variational Inequalities and Optimal Control
- Source :
- SIAM Journal on Control and Optimization. 58:3508-3532
- Publication Year :
- 2020
- Publisher :
- Society for Industrial & Applied Mathematics (SIAM), 2020.
-
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.<br />Comment: 29 pages
- Subjects :
- Class (set theory)
Control and Optimization
Applied Mathematics
multivalued solution maps
Solution set
Stability (learning theory)
Type (model theory)
Optimal control
optimal control
Mathematics - Analysis of PDEs
Optimization and Control (math.OC)
Quasi-variational inequality
Obstacle
Variational inequality
FOS: Mathematics
Applied mathematics
Mathematics - Optimization and Control
Analysis of PDEs (math.AP)
Mathematics
Subjects
Details
- ISSN :
- 10957138 and 03630129
- Volume :
- 58
- Database :
- OpenAIRE
- Journal :
- SIAM Journal on Control and Optimization
- Accession number :
- edsair.doi.dedup.....72324a8301f9651cf5b903c48365e2e1