This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These extremal principles concern measurable set-valued mappings/multifunctions with values in finite-dimensional spaces and are established in both approximate and exact forms. The obtained principles are instrumental to derive via variational approaches integral representations and upper estimates of regular and limiting normals cones to essential intersections of sets defined by measurable multifunctions, which are in turn crucial for novel applications to stochastic and semi-infinite programming.

中文翻译：

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应用于随机和半无限编程的新极值原理

本文开发了变分分析的新极值原理，其动机是应用于随机规划和半无限规划的约束问题，而没有平滑和/或凸性假设。这些极值原理涉及在有限维空间中具有值的可测量集值映射/多功能，并以近似和精确形式建立。获得的原理有助于通过变分方法推导出由可测量的多功能函数定义的集合的基本交集的正则和限制法线锥的积分表示和上限估计，这反过来对于随机和半无限编程的新应用至关重要。