由“分裂”可行性问题隐式定义的多值函数的一阶近似及其在优化中的应用
First-order approximations of multifunctions defined implicitly by "split" feasibility problems with applications to optimization
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中文总结 AI 辅助
本文研究参数化“分裂”可行性问题的解映射（多值函数）的一阶微分性质，给出其图形导数的内外近似，并探讨其在带“分裂”可行性约束的数学规划最优性条件构建中的应用。
中文摘要 AI 辅助
本文研究了某些多值函数的一阶微分性质，这些多值函数被定义为一类参数化“分裂”可行性问题的解映射。后者是一类凸可行性问题，其特定结构使其适用于工程和系统生物学等多个领域的成熟应用。因此，本文提供了该解映射的图形（ contingent）导数的内近似和外近似，这些近似以问题数据的导数形式表达。作为应用，本文还讨论了将部分成果用于构建带有“分裂”可行性约束的数学规划最优性条件的思路。
英文摘要
In the present paper, a study is made of first-order differential properties of certain multifunctions, which are defined as a solution map associated with a family of parameterized ``split" feasibility problems. The latter are a class of convex feasibility problems, whose specific structure makes them suitable for well-established applications in several areas of engineering and systems biology. As a result, inner and outer approximations of the graphical (contingent) derivative of the solution map are provided, which are expressed in terms of derivatives of the problem data. As an application, a perspective is also discussed for employing some of these achievements in the formulation of optimality conditions for mathematical programs with ``split" feasibility constraints.
