Scaled relative graphs for pairs of operators beyond classical monotonicity

Jan Quan; Alexander Bodard; Konstantinos Oikonomidis; Panagiotis Patrinos

doi:10.1016/j.ejcon.2026.101576

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arXiv · 2511.20209

Scaled relative graphs for pairs of operators beyond classical monotonicity

Jan Quan·Alexander Bodard·Konstantinos Oikonomidis·Panagiotis Patrinos

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Abstract

We introduce a generalization of the scaled relative graph (SRG) to pairs of operators, enabling the visualization of their relative incremental properties. This novel SRG framework provides the geometric counterpart for the study of nonlinear resolvents based on paired monotonicity conditions. We demonstrate that these conditions apply to linear operators composed with monotone mappings, a class that notably includes NPN transistors, allowing us to compute the response of multivalued, nonsmooth, and highly nonmonotone electrical circuits.

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Jan Quan, Alexander Bodard, Konstantinos Oikonomidis, Panagiotis Patrinos. 2025-11-25. Scaled relative graphs for pairs of operators beyond classical monotonicity. https://doi.org/10.1016/j.ejcon.2026.101576

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