77 citations · 175 across the 6 of their papers we have counts for
9 papers
Mixed-integer linear representability, disjunctions, and Chvatal functions --- modeling implications
Amitabh Basu, Kipp Martin, Christopher Thomas Ryan +1
Jeroslow and Lowe gave an exact geometric characterization of subsets of that are projections of mixed-integer linear sets, also known as MILP-representable or MILP-…
Lower bounds over Boolean inputs for deep neural networks with ReLU gates
Anirbit Mukherjee, Amitabh Basu
Motivated by the resurgence of neural networks in being able to solve complex learning tasks we undertake a study of high depth networks using ReLU gates which implement the functi…
Sparse Coding and Autoencoders
Akshay Rangamani, Anirbit Mukherjee, Amitabh Basu +4
In "Dictionary Learning" one tries to recover incoherent matrices (typically overcomplete and whose columns are assumed to be normalized) and spar…
Approximation of corner polyhedra with families of intersection cuts
Gennadiy Averkov, Amitabh Basu, Joseph Paat
We study the problem of approximating the corner polyhedron using intersection cuts derived from families of lattice-free sets in . In particular, we look at the prob…
A geometric approach to cut-generating functions
Amitabh Basu, Michele Conforti, Marco Di Summa
The cutting-plane approach to integer programming was initiated more that 40 years ago: Gomory introduced the corner polyhedron as a relaxation of a mixed integer set in tableau fo…
Maximal lattice-free convex sets in linear subspaces
Amitabh Basu, Michele Conforti, Gerard Cornuejols +1
We consider a model that arises in integer programming, and show that all irredundant inequalities are obtained from maximal lattice-free convex sets in an affine subspace. We also…