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Operational Regimes in Non-Convex Optimization: A Multiplier-Based Taxonomy

arXiv · AI, language, vision and robotics · article · Aug 31, 2026 · UTC

This paper introduces a structural taxonomy for constrained non-convex optimization based on the signature of Lagrange multipliers at KKT stationary points. Leveraging a unified game-theoretic interpretation of eight classical algorithm families--including block coordinate descent, ADMM, generalized Benders decomposition, successive convex approximation, interior-point methods, mirror descent, Frank-Wolfe, and Riemannian gradient descent--we show that the normalized multiplier vector carries an algorithm-independent structural fingerprint. Four scale-free shape features of this vector partitio

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