11 papers · 1 filter
Convex duality contracts for production-grade mathematical optimization
Juan Pablo Vielma, Ross Anderson, Joey Huchette
Deploying mathematical optimization in autonomous production systems requires precise contracts for objects returned by an optimization solver. Unfortunately, conventions on dual s…
Combinatorial Disjunctive Constraints for Obstacle Avoidance in Path Planning
Raul Garcia, Illya V. Hicks, Joey Huchette
We present a new approach for modeling avoidance constraints in 2D environments, in which waypoints are assigned to obstacle-free polyhedral regions. Constraints of this form are o…
When Deep Learning Meets Polyhedral Theory: A Survey
Joey Huchette, Gonzalo Muñoz, Thiago Serra +1
In the past decade, deep learning became the prevalent methodology for predictive modeling thanks to the remarkable accuracy of deep neural networks in tasks such as computer visio…
Building Formulations for Piecewise Linear Relaxations of Nonlinear Functions
Bochuan Lyu, Illya V. Hicks, Joey Huchette
We study mixed-integer programming formulations for the piecewise linear lower and upper bounds (in other words, piecewise linear relaxations) of nonlinear functions that can be mo…
Modeling Combinatorial Disjunctive Constraints via Junction Trees
Bochuan Lyu, Illya V. Hicks, Joey Huchette
We introduce techniques to build small ideal mixed-integer programming (MIP) formulations of combinatorial disjunctive constraints (CDCs) via the independent branching scheme. We p…
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…