A connectedness result for convex polynomial multi-objective optimization without boundedness
Year: 2026
Type: preprint
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).
Source: arXiv (Cornell University)
Author: Hieu, Vu Trung
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7216484956