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Applying set optimization to weak efficiency
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DOI：10.1007/s10479-020-03806-2.png)
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Abstract
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Set-valued extensions of vector-valued functions are used to investigate the relations between weak efficiency and variational inequalities (both Stampacchia and Minty type) which allows to apply the complete lattice framework from set optimization. Since the seminal work of Giannessi, it has been a challenge to generalize scalar results to the vector case. In this effort, some notions of generalized derivatives for vector-valued functions have been introduced, either in the form of set-valued functions or introducing appropriate notions of infinite elements in vector spaces. Switching the focus to set optimization in conlinear spaces, we propose a Dini-type derivative, that keeps the same set-valued form of the optimization problem.
Keywords:
Set optimization
Multiobjective optimization
Variational inequalities
Dini derivative
Weak efficiency
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