04 February 2026

Paper accepted @ Annali della Scuola Normale Superiore di Pisa

Glad to share that our paper Nonlinear Spectral Duality has been accepted for publication in the Annali della Scuola Normale Superiore di Pisa, Classe di Scienze.

Joint work with Dong Zhang.

The paper studies nonlinear eigenvalue problems for pairs of homogeneous convex functions, which show up in graph mining, machine learning, and network science. Using duality transforms from classical and recent convex geometry, we show that one can move from the primal to the dual nonlinear eigenvalue formulation while keeping the spectrum, the variational spectrum, and the corresponding multiplicities unchanged. This lets us recast the original optimization problem into alternative, often more treatable, dual problems, which we illustrate on graphs, nonlinear Laplacians, and distances between convex bodies.