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.
Keywords: Unified set optimization, nonlinear scalarization, oriented distance function, semicontinuity, Painlevé–Kuratowski convergence
@article{RO_2021__55_6_3603_0,
author = {Khushboo and Lalitha, C. S.},
title = {Scalarization and convergence in unified set optimization},
journal = {RAIRO. Operations Research},
pages = {3603--3616},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {6},
doi = {10.1051/ro/2021169},
mrnumber = {4348668},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2021169/}
}
TY - JOUR AU - Khushboo AU - Lalitha, C. S. TI - Scalarization and convergence in unified set optimization JO - RAIRO. Operations Research PY - 2021 SP - 3603 EP - 3616 VL - 55 IS - 6 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2021169/ DO - 10.1051/ro/2021169 LA - en ID - RO_2021__55_6_3603_0 ER -
Khushboo; Lalitha, C. S. Scalarization and convergence in unified set optimization. RAIRO. Operations Research, Tome 55 (2021) no. 6, pp. 3603-3616. doi: 10.1051/ro/2021169
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