分段多面体映射的极大单调性
Maximal monotonicity of piecewise polyhedral mappings
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中文总结 AI 辅助
研究分段多面体映射的极大单调性问题，核心方法是利用分段多面体结构绕过通常涉及相对内部交集非空的约束条件，主要贡献是解决了相关构造是否保持极大单调性的关键问题。
中文摘要 AI 辅助
分段多面体的极大单调映射源于分段线性二次凸函数和鞍函数的次微分，并用于线性二次优化及相关分裂方法的重要算法构造。这些构造是否保持极大单调性的问题至关重要。通常的答案涉及某些相对内部交集非空的约束条件，但本文表明分段多面体结构可绕过相对内部。
英文摘要
Maximal monotone mappings that are piecewise polyhedral arise from subdifferentials of convex functions and saddle functions that are piecewise linear-quadratic and enter into algorithmic constructions of importance in linear-quadratic optimization and associated splitting methods. The question of whether those constructions preserve maximal monotonicity is then crucial. The usual answers to that invoke constraint qualifications involving the nonemptiness of intersections of certain relative interiors, but it is shown here that the piecewise polyhedral structure allows the relative interiors to be bypassed.
