ABSTRACT In this paper, we give a unified treatment of two different definitions of complementarity partition of multifold conic programs introduced independently in Bonnans and Ramírez [Perturbation analysis of second-order cone programming problems, Math Program. 2005;104(2–30):205–227] for conic optimization problems, and in Peña and Roshchina [A complementarity partition theorem for multifold conic systems, Math Program. 2013;142(1–2):579–589] for homogeneous feasibility problems. We show that both can be treated within the same unified geometric framework and extend the latter notion to optimization problems. We also show that the two partitions do not coincide, and their intersection gives a seven-set index partition. Finally, we demonstrate that the partitions are preserved under the application of nonsingular linear transformations, and in particular, that a standard conversion of a second-order cone program into a semidefinite programming problem preserves the partitions.

中文翻译：

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细化多重圆锥优化问题的划分

摘要 在本文中，我们统一处理了 Bonnans 和 Ramírez 中独立引入的多重圆锥规划的互补划分的两种不同定义 [二阶锥规划问题的扰动分析，数学程序。2005;104(2-30):205-227] 用于圆锥优化问题，以及在 Peña 和 Roshchina [多重圆锥系统的互补划分定理，数学程序。2013;142(1-2):579-589] 用于同质可行性问题。我们表明两者都可以在同一个统一的几何框架内进行处理，并将后者的概念扩展到优化问题。我们还表明两个分区不重合，它们的交集给出了一个七集索引分区。最后，我们证明了在非奇异线性变换的应用下保留了分区，