摘要
在多目标最优化理论中,研究解集的拓扑结构是一个有意义的重要课题,而解集的连通性问题又是结构理论中一个重要分支。本文提出一类路拟凸多目标最优化问题,就此讨论了有效解集和弱有效解集或者是连通的,或者是路连通的。这对拟凸最优化问题关于解集的连通性,已经刻划得比较深刻(定理2—4)。其次,本文另一个主要结论(定理1)是给出了弱有效解集为连通和路连通的充分条件,这个结果对于研究弱有效解集的连通性是一个有效的工具。
The concepts of the path-quaisconvex,pathstrongly quaisconvex and path-strictly quaisconvex mappings are introduced. Under the condition that the constraint set is compact and pathwise connected while the objcetive function is continuous and path-quaisconvex,we prove the connectedness resultes of the efficient solution and weakly efficient solution sets to multiobjective optimization problems.
