论文标题
解决设定最小化问题的INF译本
The inf-translation for solving set minimization problems
论文作者
论文摘要
设置和矢量值的优化问题可以重新形成为完整的晶格值问题。这具有几个优点，其中之一是存在一个清晰的解决方案概念，其中包括成就作为immim（不存在于传统矢量优化理论中），而最小化是两个潜在的不同特征。任务是找到足够大以生成量最大的设置，同时又足够小，仅包括最小化器。 在本文中，基于Inf译的此类集合的最佳条件是在抽象框架内给出的。 INF译本将解决方案设置降低到单个点，进而将其应用于应用更多标准程序。对于具有完整晶格中值的函数，在重点放在凸问题上的情况下，提供标态结果。媒介优化问题，特别是变异问题的矢量计算，作为示例讨论。
Set- and vector-valued optimization problems can be re-formulated as complete lattice-valued problems. This has several advantages, one of which is the existence of a clear-cut solution concept which includes the attainment as the infimum (not present in traditional vector optimization theory) and minimality as two potentially different features. The task is to find a set which is large enough to generate the infimum but at the same time small enough to include only minimizers. In this paper, optimality conditions for such sets based on the inf-translation are given within an abstract framework. The inf-translation reduces the solution set to a single point which in turn admits the application of more standard procedures. For functions with values in complete lattices of sets, scalarization results are provided where the focus is on convex problems. Vector optimization problems, in particular a vectorial calculus of variations problem, are discussed as examples.
