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Mathematics > Optimization and Control

arXiv:2511.20209 (math)
[Submitted on 25 Nov 2025 (v1), last revised 21 Aug 2026 (this version, v2)]

Title:Scaled relative graphs for pairs of operators beyond classical monotonicity

Authors: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.
Comments: Accepted at the 2026 ECC Special Issue of the European Journal of Control
Subjects: Optimization and Control (math.OC)
Cite as: arXiv:2511.20209 [math.OC]
  (or arXiv:2511.20209v2 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2511.20209
Related DOI: https://doi.org/10.1016/j.ejcon.2026.101576

Submission history

From: Jan Quan [view email]
[v1] Tue, 25 Nov 2025 11:34:17 UTC (1,538 KB)
[v2] Fri, 21 Aug 2026 12:50:27 UTC (1,588 KB)
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