Applying set optimization to weak efficiency

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...

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Bibliographic Details
Published in:Annals of operations research 2021, Vol.296 (1-2), p.779-801
Main Authors: Crespi, Giovanni P., Schrage, Carola
Format: Article
Language:English
Subjects:
Business and Management
Combinatorics
Inequalities (Mathematics)
Mathematical optimization
Operations research
Operations Research/Decision Theory
Optimization
S.i.: Mopgp 2017
Theory of Computation
Vector spaces
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Summary: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.
ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-020-03806-2