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

Javier I. Madariaga () and Héctor Ramírez ()
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Javier I. Madariaga: North Carolina State University
Héctor Ramírez: Universidad de Chile

Journal of Optimization Theory and Applications, 2025, vol. 204, issue 1, No 15, 27 pages

Abstract: Abstract 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.

Keywords: Conic programming; Complementarity constraints; Stationary point; Facial stationarity; 49J52; 49K27; 90C33 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-024-02562-8

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