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arXiv · 2610.01029

A connectedness result for convex polynomial multi-objective optimization without boundedness

Vu Trung Hieu
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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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Vu Trung Hieu. 2026-10-01. A connectedness result for convex polynomial multi-objective optimization without boundedness. https://arxiv.org/abs/2610.01029

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