A Smoothed Augmented Lagrangian Method for Mathematical Programs with Vertical Complementarity Constraints
Year: 2026
Type: preprint
Abstract: We propose a smoothed augmented Lagrangian method (ALM) for solving mathematical programs with vertical complementarity constraints (VCCs). The augmented Lagrangian function involving the VCCs is smoothed by the Lasry--Lions double envelope, which is an extension of the Moreau envelope that enjoys enhanced smoothness properties. This construction yields a smooth unconstrained subproblem within the ALM framework that can be efficiently solved by many fast optimization algorithms. In the limiting setting, we establish global convergence to Mordukhovich- and Clarke-stationary points. For the convergence rate, we show that, under appropriate assumptions, the smoothed ALM achieves Q-linear convergence. We further provide a worst-case iteration complexity analysis for computing an approximate stationary point of the original problem or of an associated feasibility problem. Preliminary numerical experiments demonstrate the effectiveness of the proposed method.
Source: arXiv (Cornell University)
Institutions: KU Leuven, Kyushu University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G2630444842, G3742396460, Learning to optimize nonconvex problems: provably and efficiently, Taming Nonconvexity in Structured Low-Rank Optimization., Rethinking Transformers Through Duality Principles, From model-based to data-driven: signal processing and control engineering for nonlinear systems
OpenAlex ID: W7221804996