5 papers
Positive Univariate Polynomials: SOS certificates, algorithms, bit complexity, and T-systems
MatÃas Bender, Philipp Di Dio, Elias Tsigaridas
We consider certificates of positivity for univariate polynomials with rational coefficients that are positive over (an interval of)~. Such certificates take the form o…
Semidefinite network games: multiplayer minimax and complementarity problems
Constantin Ickstadt, Thorsten Theobald, Elias Tsigaridas +1
Network games provide a powerful framework for modeling agent interactions in networked systems, where players are represented by nodes in a graph and their payoffs depend on the a…
Solving bihomogeneous polynomial systems with a zero-dimensional projection
MatÃas Bender, Laurent Busé, Carles Checa +1
We study bihomogeneous systems defining, non-zero dimensional, biprojective varieties for which the projection onto the first group of variables results in a finite set of points.…
Nash equilibria in semidefinite games and Lemke-Howson paths
Constantin Ickstadt, Thorsten Theobald, Elias Tsigaridas +1
We consider an algorithmic framework for two-player non-zero-sum semidefinite games, where each player's strategy is a positive semidefinite matrix with trace one. We formulate the…
Bigraded Castelnuovo-Mumford regularity and Gröbner bases
MatÃas Bender, Laurent Busé, Carles Checa +1
We study the relation between the bigraded Castelnuovo-Mumford regularity of a bihomogeneous ideal in the coordinate ring of the product of two projective spaces and the bidegr…