Abstract
A controlled sweeping process with prox-regular set, \(W^{1,2}\)-controls, and separable endpoints constraints is considered in this paper. Existence of optimal solutions is established and local optimality conditions are derived via strong converging continuous approximations, whose state entirely resides in the interior of the prox-regular set. Consequently, subdifferentials smaller than the standard ones are now employed in the optimality results.
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The authors wish to thank the Editor and the anonymous referees for their valuable comments that greatly improved the paper.
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Communicated by Giovanni Colombo.
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Chadi Nour and Vera Zeidan contributed equally to this work. This paper is dedicated to our PhD advisor Francis H. Clarke on the occasion of his 75th birthday.
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Nour, C., Zeidan, V. A Control Space Ensuring the Strong Convergence of Continuous Approximation for a Controlled Sweeping Process. Set-Valued Var. Anal 31, 23 (2023). https://doi.org/10.1007/s11228-023-00686-z
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DOI: https://doi.org/10.1007/s11228-023-00686-z
Keywords
- Controlled sweeping process
- Prox-regular sets
- Necessary optimality conditions
- Local minimizers
- Strong convergence
- Continuous approximations
- Nonsmooth analysis