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<p>This paper studies stationary points in mathematical programs with cone complementarity constraints (CMPCC). We begin by reviewing various formulations of CMPCC and revisiting definitions for Bouligand, proximal strong, regular strong, Wachsmuth’s strong, <i>L</i>-strong, weak, as well as Mordukhovich and Clarke stationary points, establishing a comprehensive framework for CMPCC. Building on key principles related to cone faces and their properties, we introduce a novel stationarity concept, facial stationarity, which naturally extends the weak stationarity condition in the CMPCC context. Finally, we analyze the hierarchical relations between these different types of stationary points.</p>

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Facial Approach for Constructing Stationary Points for Mathematical Programs with Cone Complementarity Constraints

  • 期刊论文

  • 发表日期：

    2025年1月3日

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  • Javier I. Madariaga,
  • Héctor Ramírez

摘要

This paper studies stationary points in mathematical programs with cone complementarity constraints (CMPCC). We begin by reviewing various formulations of CMPCC and revisiting definitions for Bouligand, proximal strong, regular strong, Wachsmuth’s strong, L-strong, weak, as well as Mordukhovich and Clarke stationary points, establishing a comprehensive framework for CMPCC. Building on key principles related to cone faces and their properties, we introduce a novel stationarity concept, facial stationarity, which naturally extends the weak stationarity condition in the CMPCC context. Finally, we analyze the hierarchical relations between these different types of stationary points.