无限维空间拟凸映射多目标最优化问题解集的连通性  

THE CONNECTEDNESS OF SOLUTION SETS FOR A QUASICONVEX OPTIMIZATION IN INFINITE DIMENSIONAL SPACES

作　　者：博万涛 周昆平[2] 

机构地区：[1]南昌大学数学系,南昌330047 [2]复旦大学统计运筹系,上海200433

出　　处：《应用数学学报》1997年第1期137-145,145,共9页Acta Mathematicae Applicatae Sinica

摘　　要：本文在一个无限格中引入了拟凸、强拟凸和严格拟凸映射．并在约束集为紧凸条件下，证明了相应的多目标规划问题之有效解集和弱有效解集连通性结果．One of the key questions of multiobjective optimization theory is to investigatethe connectedness of solution sets. In this paper, the concept of quasiconvex, stronglyquasiconvex and strictly quasiconvex mappings are introduced. Under the condition thatthe constraint set is compact and convex while the objective function is continuous andquasiconvex (strongly and strictly quasiconvex), we prove the connectedness results of weaklyefficient solution sets (efficient sets) to multiobjective optimization problems. Particularly,we prove that if the objective function is strongly quasiconvex, then the efficient solutionsets is pathwise connected.

关 键 词：拟凸规划 拟凸映射 多目标最优化 连通性 解集 

分 类 号：O221[理学—运筹学与控制论]