234 citations · 639 across the 28 of their papers we have counts for
5 papers · 1 filter
A game theory approach to the existence and uniqueness of nonlinear Perron-Frobenius eigenvectors
Marianne Akian, Stéphane Gaubert, Antoine Hochart
We establish a generalized Perron-Frobenius theorem, based on a combinatorial criterion which entails the existence of an eigenvector for any nonlinear order-preserving and positiv…
Log-sum-exp neural networks and posynomial models for convex and log-log-convex data
Giuseppe C. Calafiore, Stephane Gaubert, Corrado Possieri
We show in this paper that a one-layer feedforward neural network with exponential activation functions in the inner layer and logarithmic activation in the output neuron is an uni…
A convergent hierarchy of non-linear eigenproblems to compute the joint spectral radius of nonnegative matrices
Stephane Gaubert, Nikolas Stott
We show that the joint spectral radius of a finite collection of nonnegative matrices can be bounded by the eigenvalue of a non-linear operator. This eigenvalue coincides with the…
Spectral inequalities for nonnegative tensors and their tropical analogues
Shmuel Friedland, Stéphane Gaubert
We extend some characterizations and inequalities for the eigenvalues of nonnegative matrices, such as Donsker-Varadhan, Friedland-Karlin, Karlin-Ost inequalities, to nonnegative t…
Condition numbers of stochastic mean payoff games and what they say about nonarchimedean semidefinite programming
Xavier Allamigeon, Stéphane Gaubert, Ricardo D. Katz +1
Semidefinite programming can be considered over any real closed field, including fields of Puiseux series equipped with their nonarchimedean valuation. Nonarchimedean semidefinite…