【摘要】 本文研究的是约束集值优化问题的高价最优性条件.首先通过借助集值映射的Stud-niarski导数和严格局部有效性,讨论了集值优化问题的高阶必要条件和充分条件.对于充分条件,初始空间必须是有限维的.其次在初始空间和目标空间是有限维的以及集值映射是m阶稳定的条件下,也得到了此约束集值优化问题的高阶最优性条件.更多还原

【Abstract】 This paper deals with higher-order optimality conditions of a set-valued optimization problem(SOP) whose constraint condition is determined by a fixed set.By virtue of Studniarski derivatives of set-valued maps and strict local efficiency,higher-order necessary and sufficient optimality conditions for SOP are obtained.For the sufficient conditions,the initial space must be finite dimensional.Higher-order optimality conditions for SOP are also investigated under the conditions that the initial and objective spaces are finite dimensional and the multifunction involved is mth-order stable.更多还原