发表机构
Ho Chi Minh City University of Technology（胡志明市理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明凸多项式多目标优化问题的弱Pareto解集在无有界性和约束规范条件下仍连通，并由此得出凸二次情形解集路径连通，回答了Yen的开放问题。
AI 中文摘要
我们证明了具有凸多项式目标函数和约束条件的多目标优化问题的弱Pareto解集是连通的，该证明既不假设约束集有界，也不假设约束规范成立。由于该解集是半代数的，其连通性意味着当它非空时是路径连通的。特别地，凸二次多目标优化问题具有连通的弱Pareto解集；这回答了N. D. Yen在《向量优化的最新进展》（Springer, 2012）中提出的一个开放问题的弱Pareto部分。
英文摘要
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).
Comments10 pages; 1 figure;
