Approximations for Pareto and Proper Pareto solutions and their KKT conditions. Kesarwani, P., Shukla, P. K., Dutta, J., & Deb, K. Mathematical Methods of Operations Research, 96(1):123–148, August, 2022. 1 citations (Semantic Scholar/DOI) [2023-06-19]Paper doi abstract bibtex In this article, we focus on approximate solution concepts in multiobjective optimization. We begin with well-known notions of approximate Pareto and weak Pareto solutions and the key result deduced about these notions is that any sequence converging to a weak Pareto minimizer satisfies an approximate Karush-Kuhn-Tucker (KKT) type necessary optimality condition. We then focus on the notion of approximate Geoffrion proper solutions with a preset bound and characterize them entirely through saddle-point type conditions for the problem with convex data. We also describe the approximate Benson proper solutions completely for a multiobjective problem having convex data through KKT type conditions.
@article{kesarwani_approximations_2022,
title = {Approximations for {Pareto} and {Proper} {Pareto} solutions and their {KKT} conditions},
volume = {96},
issn = {1432-2994, 1432-5217},
url = {https://link.springer.com/10.1007/s00186-022-00787-9},
doi = {10.1007/s00186-022-00787-9},
abstract = {In this article, we focus on approximate solution concepts in multiobjective optimization. We begin with well-known notions of approximate Pareto and weak Pareto solutions and the key result deduced about these notions is that any sequence converging to a weak Pareto minimizer satisfies an approximate Karush-Kuhn-Tucker (KKT) type necessary optimality condition. We then focus on the notion of approximate Geoffrion proper solutions with a preset bound and characterize them entirely through saddle-point type conditions for the problem with convex data. We also describe the approximate Benson proper solutions completely for a multiobjective problem having convex data through KKT type conditions.},
language = {en},
number = {1},
urldate = {2023-06-17},
journal = {Mathematical Methods of Operations Research},
author = {Kesarwani, P. and Shukla, P. K. and Dutta, J. and Deb, K.},
month = aug,
year = {2022},
note = {1 citations (Semantic Scholar/DOI) [2023-06-19]},
keywords = {/unread},
pages = {123--148},
}
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