PreprintCC BY 4.0arXiv
A connectedness result for convex polynomial multi-objective optimization without boundedness
Abstract
We prove that the weak Pareto solution set of a multi-objective optimization problem with convex polynomial objectives and constraints is connected, assuming neither boundedness of the constraint set nor a constraint qualification. Since this set is semi-algebraic, its connectedness implies that it is path-connected whenever it is nonempty. In particular, convex quadratic multi-objective optimization problems have connected weak Pareto solution sets; this answers the weak Pareto part of an open question posed by N.~D.~Yen in \emph{Recent Developments in Vector Optimization} (Springer, 2012).
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BibTeX
@misc{hieu2026connectedness,
title = {{A connectedness result for convex polynomial multi-objective optimization without boundedness}},
author = {Vu Trung Hieu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01029},
eprint = {2610.01029},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01029},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A connectedness result for convex polynomial multi-objective optimization without boundedness
AU - Vu Trung Hieu
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01029
UR - https://arxiv.org/abs/2610.01029
AB - We prove that the weak Pareto solution set of a multi-objective optimization problem with convex polynomial objectives and constraints is connected, assuming neither boundedness of the constraint set nor a constraint qualification. Since this set is semi-algebraic, its connectedness implies that it is path-connected whenever it is nonempty. In particular, convex quadratic multi-objective optimization problems have connected weak Pareto solution sets; this answers the weak Pareto part of an open question posed by N.~D.~Yen in \emph{Recent Developments in Vector Optimization} (Springer, 2012).
ER -