6 papers
On the equivalence of a Hessian-free inequality and Lipschitz continuous Hessian
Radu I. Boţ, Minh N. Dao, Tianxiang Liu +2
It is known that if a twice differentiable function has a Lipschitz continuous Hessian, then its gradients satisfy a Jensen-type inequality. In particular, this inequality is Hessi…
Inner approximations of convex sets and intersections of projectionally exposed cones
Bruno F. Lourenço, Vera Roshchina, James Saunderson
A convex cone is said to be projectionally exposed (p-exposed) if every face arises as a projection of the original cone. It is known that, in dimension at most four, the intersect…
Faces of homogeneous cones and applications to homogeneous chordality
João Gouveia, Masaru Ito, Bruno F. Lourenço
A convex cone is said to be homogeneous if its group of automorphisms acts transitively on its relative interior. Important examples of homogeneous cones include symm…
Minimal hyperbolic polynomials and ranks of homogeneous cones
João Gouveia, Masaru Ito, Bruno F. Lourenço
The starting point of this paper is the computation of minimal hyperbolic polynomials of duals of cones arising from chordal sparsity patterns. From that, we investigate the relati…
A framework for large scale phylogenetic analysis
Bruno Lourenço
With growing exchanges of people and merchandise between countries, epidemics have become an issue of increasing importance and huge amounts of data are being collected every day.…
A weak constraint qualification for conic programs and a problem on duality gap
Bruno F. Lourenço
We discuss a weak constraint qualification for conic linear programs and its applications for a few classes of cones. This constraint qualification is used to give a solution to a…