9 papers
Tropical low-rank approximation and application to optimal control of N-body systems
Marianne Akian, Stephane Gaubert, Shanqing Liu +1
We study the approximation of the value function of deterministic optimal control problems with fixed initial state, motivated by \(N\)-body systems. In this setting, the action fu…
Linear algebra over T-pairs
Marianne Akian, Stephane Gaubert, Louis Rowen
This is part of an ongoing project to find a general algebraic framework for semiring theory. The structure theory of semirings is quite challenging, largely because of the lack of…
Dynamics of multidimensional Simple Clock Auctions
Jad Zeroual, Marianne Akian, Aurélien Bechler +2
Simple Clock Auctions (SCA) are a mechanism commonly used in spectrum auctions to sell lots of frequency bandwidths. We study such an auction with one player having access to perfe…
Optimal strategy against straightforward bidding in clock auctions
Jad Zeroual, Marianne Akian, Aurélien Bechler +2
We study a model of auction representative of the 5G auction in France. We determine the optimal strategy of a bidder, assuming that the valuations of competitors are unknown to th…
Order isomorphisms of sup-stable function spaces: continuous, Lipschitz, c-convex, and beyond
Pierre-Cyril Aubin-Frankowski, Stéphane Gaubert
There have been many parallel streams of research studying order isomorphisms of some specific sets of functions from a set to , such as the se…
Spectral Properties of Positive Definite Matrices over Symmetrized Tropical Algebras and Valued Ordered fields
Marianne Akian, Stephane Gaubert, Dariush Kiani +1
We investigate the properties of positive definite and positive semi-definite symmetric matrices within the framework of symmetrized tropical algebra, an extension of tropical alge…