The Convex Relaxation Barrier, Revisited: Tightened Single-Neuron Relaxations for Neural Network Verification

no code implementations • NeurIPS 2020 • Christian Tjandraatmadja, Ross Anderson, Joey Huchette, Will Ma, Krunal Patel, Juan Pablo Vielma

We improve the effectiveness of propagation- and linear-optimization-based neural network verification algorithms with a new tightened convex relaxation for ReLU neurons.

Solving natural conic formulations with Hypatia.jl

1 code implementation • 3 May 2020 • Chris Coey, Lea Kapelevich, Juan Pablo Vielma

For optimization problems from a variety of applications, we introduce natural formulations using these exotic cones, and we show that the natural formulations are simpler and lower-dimensional than the equivalent extended formulations.

Optimization and Control 90-04, 90C22, 90C23, 90C25, 90C51

Strong mixed-integer programming formulations for trained neural networks

no code implementations • 20 Nov 2018 • Ross Anderson, Joey Huchette, Christian Tjandraatmadja, Juan Pablo Vielma

We present an ideal mixed-integer programming (MIP) formulation for a rectified linear unit (ReLU) appearing in a trained neural network.

Strong convex relaxations and mixed-integer programming formulations for trained neural networks

1 code implementation • 5 Nov 2018 • Ross Anderson, Joey Huchette, Christian Tjandraatmadja, Juan Pablo Vielma

We present strong convex relaxations for high-dimensional piecewise linear functions that correspond to trained neural networks.

Optimization and Control 90C11

Outer Approximation With Conic Certificates For Mixed-Integer Convex Problems

5 code implementations • 15 Aug 2018 • Chris Coey, Miles Lubin, Juan Pablo Vielma

Using properties of the conic certificates, we show that the $\mathcal{K}^*$ cuts imply certain practically-relevant guarantees about the quality of the polyhedral relaxations, and demonstrate how to maintain helpful guarantees when the LP solver uses a positive feasibility tolerance.

Optimization and Control

Picking Winners in Daily Fantasy Sports Using Integer Programming

5 code implementations • 6 Apr 2016 • David Scott Hunter, Juan Pablo Vielma, Tauhid Zaman

Building on this, we then consider a scenario where the entries are given by sums of constrained resources and present an integer programming formulation to construct the entries.

Other Statistics

Extended Formulations in Mixed-integer Convex Programming

2 code implementations • 20 Nov 2015 • Miles Lubin, Emre Yamangil, Russell Bent, Juan Pablo Vielma

We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP).

Optimization and Control