Abstract
In this paper state constrained optimal control problems governed by parabolic evolution equations are studied. Our purpose is to obtain a (first-order) decoupled optimality system (that ensures the Lagrange multipliers existence). In a first step we are led to Slater-like assumptions and we are then allowed to extend the application field of the decoupled system we obtain. With a weaker assumption the existence of Lagrange multipliers (that are measures) for nonqualified problems may be established.
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Communicated by A. Bensoussan
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Bergounioux, M. Optimal control of parabolic problems with state constraints: a penalization method for optimality conditions. Appl Math Optim 29, 285–307 (1994). https://doi.org/10.1007/BF01189479
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DOI: https://doi.org/10.1007/BF01189479
Key words
- Optimal control
- Optimality conditions
- State constraints
- Lagrange multipliers
- Parabolic systems
- Penalization