1.3k citations · 1.4k across the 16 of their papers we have counts for
20 papers
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…
Neural Network Verification as Piecewise Linear Optimization: Formulations for the Composition of Staircase Functions
Tu Anh-Nguyen, Joey Huchette
We present a technique for neural network verification using mixed-integer programming (MIP) formulations. We derive a \emph{strong formulation} for each neuron in a network using…
JuMP 1.0: Recent improvements to a modeling language for mathematical optimization
Miles Lubin, Oscar Dowson, Joaquim Dias Garcia +3
JuMP is an algebraic modeling language embedded in the Julia programming language. JuMP allows users to model optimization problems of a variety of kinds, including linear programm…
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…
The Convex Relaxation Barrier, Revisited: Tightened Single-Neuron Relaxations for Neural Network Verification
Christian Tjandraatmadja, Ross Anderson, Joey Huchette +3
We improve the effectiveness of propagation- and linear-optimization-based neural network verification algorithms with a new tightened convex relaxation for ReLU neurons. Unlike pr…
Contextual Reserve Price Optimization in Auctions via Mixed-Integer Programming
Joey Huchette, Haihao Lu, Hossein Esfandiari +1
We study the problem of learning a linear model to set the reserve price in an auction, given contextual information, in order to maximize expected revenue from the seller side. Fi…
A geometric way to build strong mixed-integer programming formulations
Joey Huchette, Juan Pablo Vielma
We give an explicit geometric way to build mixed-integer programming (MIP) formulations for unions of polyhedra. The construction is simply described in terms of spanning hyperplan…
Strong mixed-integer programming formulations for trained neural networks
Ross Anderson, Joey Huchette, Christian Tjandraatmadja +1
We present an ideal mixed-integer programming (MIP) formulation for a rectified linear unit (ReLU) appearing in a trained neural network. Our formulation requires a single binary v…
Strong mixed-integer programming formulations for trained neural networks
Ross Anderson, Joey Huchette, Will Ma +2
We present strong mixed-integer programming (MIP) formulations for high-dimensional piecewise linear functions that correspond to trained neural networks. These formulations can be…
A mixed-integer branching approach for very small formulations of disjunctive constraints
Joey Huchette, Juan Pablo Vielma
An important problem in optimization is the construction of mixed-integer programming (MIP) formulations of disjunctive constraints that are both strong and small. Motivated by low…
Nonconvex piecewise linear functions: Advanced formulations and simple modeling tools
Joey Huchette, Juan Pablo Vielma
We present novel mixed-integer programming (MIP) formulations for optimization over nonconvex piecewise linear functions. We exploit recent advances in the systematic construction…
A combinatorial approach for small and strong formulations of disjunctive constraints
Joey Huchette, Juan Pablo Vielma
We present a framework for constructing strong mixed-integer programming formulations for logical disjunctive constraints. Our approach is a generalization of the logarithmically-s…
Beating the SDP bound for the floor layout problem: A simple combinatorial idea
Joey Huchette, Santanu S. Dey, Juan Pablo Vielma
For many mixed-integer programming (MIP) problems, high-quality dual bounds can be obtained either through advanced formulation techniques coupled with a state-of-the-art MIP solve…
Strong mixed-integer formulations for the floor layout problem
Joey Huchette, Santanu S. Dey, Juan Pablo Vielma
The floor layout problem (FLP) tasks a designer with positioning a collection of rectangular boxes on a fixed floor in such a way that minimizes total communication costs between t…
JuMP: A Modeling Language for Mathematical Optimization
Iain Dunning, Joey Huchette, Miles Lubin
JuMP is an open-source modeling language that allows users to express a wide range of optimization problems (linear, mixed-integer, quadratic, conic-quadratic, semidefinite, and no…
Extended Formulations in Mixed Integer Conic Quadratic Programming
Juan Pablo Vielma, Iain Dunning, Joey Huchette +1
In this paper we consider the use of extended formulations in LP-based algorithms for mixed integer conic quadratic programming (MICQP). Extended formulations have been used by Vie…