We present necessary and sufficient optimality conditions for the minimization of pseudoconvex functions over convex intersections of non necessarily convex sets. To this aim, we use the notion of local normal cone to a closed set at a point, due to Linh and Penot (SIAM J Optim 17:500–510, 2006). The technique we use to obtain the optimality conditions is based on the so called canonical representation of a closed set by means of its associated oriented distance function.

中文翻译：

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非必须凸集相交上凸问题的最优性条件

我们为非凸集的凸交点上的伪凸函数的最小化提供了必要和充分的最优条件。为此，由于Linh和Penot（SIAM J Optim 17：500-510，2006），我们将局部法线锥的概念用于某个点的封闭集合。我们用于获得最佳条件的技术基于封闭集的所谓规范表示，借助其关联的定向距离函数。