15 citations · 52 across the 12 of their papers we have counts for
12 papers
Edge expansion of a graph: SDP-based computational strategies
Akshay Gupte, Melanie Siebenhofer, Angelika Wiegele
Computing the edge expansion of a graph is a famously hard combinatorial problem for which there have been many approximation studies. We present two variants of exact algorithms u…
Multilinear formulations for computing Nash equilibrium of multi-player matrix games
Miriam Fischer, Akshay Gupte
We present multilinear and mixed-integer multilinear programs to find a Nash equilibrium in multi-player noncooperative games. We compare the formulations to common algorithms in G…
Large independent sets in recursive Markov random graphs
Akshay Gupte, Yiran Zhu
Computing the maximum size of an independent set in a graph is a famously hard combinatorial problem that has been well-studied for various classes of graphs. When it comes to rand…
Polyhedral Analysis of Symmetric Multilinear Polynomials over Box Constraints
Yibo Xu, Warren Adams, Akshay Gupte
It is well-known that the convex and concave envelope of a multilinear polynomial over a box are polyhedral functions. Exponential-sized extended and projected formulations for the…
On strong duality, theorems of the alternative, and projections in conic optimization
Temitayo Ajayi, Akshay Gupte, Amin Khademi +1
A conic program is the problem of optimizing a linear function over a closed convex cone intersected with an affine preimage of another cone. We analyse three constraint qualificat…
Branch-and-bound for biobjective mixed-integer linear programming
Nathan Adelgren, Akshay Gupte
We present a generic branch-and-bound algorithm for finding all the Pareto solutions of a biobjective mixed-integer linear program. The main contributions are new algorithms for ob…
Error bounds for monomial convexification in polynomial optimization
Warren Adams, Akshay Gupte, Yibo Xu
Convex hulls of monomials have been widely studied in the literature, and monomial convexifications are implemented in global optimization software for relaxing polynomials. Howeve…
Extended formulations for convex hulls of graphs of bilinear functions
Akshay Gupte, Thomas Kalinowski, Fabian Rigterink +1
We consider the problem of characterizing the convex hull of the graph of a bilinear function on the -dimensional unit cube . Extended formulations for this convex…
On Dantzig figures from graded lexicographic orders
Akshay Gupte, Svetlana Poznanović
We construct two families of Dantzig figures, which are -polytopes with an antipodal vertex pair, from convex hulls of initial subsets for the graded lexicographic (grlex)…
On lexicographic approximations of integer programs
Michael Eldredge, Akshay Gupte
We use the lexicographic order to define a hierarchy of primal and dual bounds on the optimum of a bounded integer program. These bounds are constructed using lex maximal and minim…
Convex hulls of superincreasing knapsacks and lexicographic orderings
Akshay Gupte
We consider bounded integer knapsacks where the weights and variable upper bounds together form a superincreasing sequence. The elements of this superincreasing knapsack are exactl…
Efficient storage of Pareto points in biobjective mixed integer programming
Nathan Adelgren, Pietro Belotti, Akshay Gupte
In biobjective mixed integer linear programs (BOMILPs), two linear objectives are minimized over a polyhedron while restricting some of the variables to be integer. Since many of t…