带变序结构的锥约束向量优化问题在工程分析、资源分配、偏好建模等问题中有着重要的应用。文章研究带变序结构的锥约束向量优化问题的对偶理论,用非线性的标量化泛函定义了与所研究问题相关的拉格朗日函数,讨论了这个拉格朗日函数鞍点的性质,并且根据拉格朗日函数的鞍点来刻画给定锥约束向量优化问题的Benson型真极小解。此外,还根据拉格朗日函数定义了给定锥约束向量优化问题相应的对偶集,并在稳定性假设下证明了相关的强对偶结果。The problem of cone-constraint vector optimization with variable ordering structures has important applications in engineering analysis, resource allocation, and preference modeling. This paper studies the dual theory of the cone-constrained vector optimization problem with variable ordering structures. The Lagrangian associated with the nonlinear scalar function is defined. The saddle point’s properties of this Lagrangian are discussed, and the properly minimal solution in the sense of Benson is characterized according to the saddle point of the Lagrangian. Furthermore, the corresponding dual set of the given cone-constrained vector optimization problem is defined according to the Lagrangian, and the associated strong dual results are proved under the assumption of stability.
