7 citations · 8 across the 7 of their papers we have counts for
8 papers · 1 filter
Integer Maximization over Balls: Hardness and Exact Algorithms
Cinar Ari, Robert Hildebrand
We study the problem of maximizing a linear function over the integer points of an origin-centered ball, which we call \BallIPp{p}. For every fixed integer , we pro…
Curvature batching gives single-exponential integer quadratic programming
Cinar Ari, Robert Hildebrand
Integer Quadratic Programming (IQP), , is a fundamental problem in combinatorial optimization. While the convex and concave special…
Optimal triangulations for piecewise linear approximations of non-convex variable products
Robert Burlacu, Lukas Hager, Robert Hildebrand
We show optimal triangulations for piecewise linear (PWL) approximations of indefinite quadratic functions over the plane. Optimal triangulations have minimum triangle density whil…
Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. IV. The General Unimodular Two-Dimensional Case
Robert Hildebrand, Matthias Köppe, Luze Xu
We study an abstract setting for cutting planes for integer programming called the infinite group problem. In this abstraction, cutting planes are computed via cut generating funct…
Compact mixed-integer programming relaxations in quadratic optimization
Ben Beach, Robert Hildebrand, Joey Huchette
We present a technique for producing valid dual bounds for nonconvex quadratic optimization problems. The approach leverages an elegant piecewise linear approximation for univariat…
An Approximate Method for the Optimization of Long-Horizon Tank Blending and Scheduling Operations
Benjamin Beach, Robert Hildebrand, Kimberly Ellis +1
We address a challenging tank blending and scheduling problem regarding operations for a chemical plant. We model the problem as a nonconvex MIQCP, then approximate this model as a…