Volume 55, Number 6, November-December 2021
|Page(s)||3603 - 3616|
|Published online||08 December 2021|
Scalarization and convergence in unified set optimization
Department of Mathematics, University of Delhi, Delhi 110007, India
2 Department of Mathematics, University of Delhi South Campus, Benito Juarez Road, New Delhi 110021, India
* Corresponding author: email@example.com
Accepted: 16 November 2021
This paper deals with scalarization and stability aspects for a unified set optimization problem. We provide characterization for a unified preference relation and the corresponding unified minimal solution in terms of a generalized oriented distance function of the sup-inf type. We establish continuity of a function associated with the generalized oriented distance function and provide an existence result for the unified minimal solution. We establish Painlevé–Kuratowski convergence of minimal solutions of a family of scalar problems to the minimal solutions of the unified set optimization problem.
Mathematics Subject Classification: 54C60 / 90C26 / 49J53
Key words: Unified set optimization / nonlinear scalarization / oriented distance function / semicontinuity / Painlevé–Kuratowski convergence
© The authors. Published by EDP Sciences, ROADEF, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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