欧几里德若当代数向量优化问题的谱标量化

Scalarization of Vector Optimization on Euclidean Jordan Algebra

本文主要研究欧几里德若当代数向量优化的谱标量化.引入了一个新的标量函数-谱标量函数,给出了此谱函数在欧几里德若当代数中具有K-增性(相应的,严格K-增性)的充分条件,从而使得满足此条件的谱标量优化问题的解(即谱标量解)为向量优化问题的K-弱有效解(相应的,K-有效解).在适当的条件下,我们证明了谱标量解集值映射的上半连续性.同时,还给出了谱标量解集值映射满足下半连续的充分必要条件.

In this paper,we study the scalarization over Euclidean Jordan algebra vector optimization problem.We introduce a new scalar function-spectral scalar function and study it＇s K-increasing property or strictly K-increasing property.Under some suitable conditions,we prove the upper semi-continuity of the spectral scalar solution mapping. Meanwhile,we also provide the necessary and sufficient conditions which guarantee the lower semi-continuity of spectral scalar solution mapping.