91 citations · 113 across the 13 of their papers we have counts for
14 papers
Proximal Projection Method for Stable Linearly Constrained Optimization
Howard Heaton
Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified to…
Laplace Meets Moreau: Smooth Approximation to Infimal Convolutions Using Laplace's Method
Ryan J. Tibshirani, Samy Wu Fung, Howard Heaton +1
We study approximations to the Moreau envelope -- and infimal convolutions more broadly -- based on Laplace's method, a classical tool in analysis which ties certain integrals to s…
Differentiating Through Integer Linear Programs with Quadratic Regularization and Davis-Yin Splitting
Daniel McKenzie, Samy Wu Fung, Howard Heaton
In many applications, a combinatorial problem must be repeatedly solved with similar, but distinct parameters. Yet, the parameters are not directly observed; only contextual da…
A Hamilton-Jacobi-based Proximal Operator
Stanley Osher, Howard Heaton, Samy Wu Fung
First-order optimization algorithms are widely used today. Two standard building blocks in these algorithms are proximal operators (proximals) and gradients. Although gradients can…
Explainable AI via Learning to Optimize
Howard Heaton, Samy Wu Fung
Indecipherable black boxes are common in machine learning (ML), but applications increasingly require explainable artificial intelligence (XAI). The core of XAI is to establish tra…
Global Solutions to Nonconvex Problems by Evolution of Hamilton-Jacobi PDEs
Howard Heaton, Samy Wu Fung, Stanley Osher
Computing tasks may often be posed as optimization problems. The objective functions for real-world scenarios are often nonconvex and/or nondifferentiable. State-of-the-art methods…
Operator Splitting for Learning to Predict Equilibria in Convex Games
Daniel McKenzie, Howard Heaton, Qiuwei Li +3
Systems of competing agents can often be modeled as games. Assuming rationality, the most likely outcomes are given by an equilibrium (e.g. a Nash equilibrium). In many practical s…
Feasibility-based Fixed Point Networks
Howard Heaton, Samy Wu Fung, Aviv Gibali +1
Inverse problems consist of recovering a signal from a collection of noisy measurements. These problems can often be cast as feasibility problems; however, additional regularizatio…
Learning to Optimize: A Primer and A Benchmark
Tianlong Chen, Xiaohan Chen, Wuyang Chen +4
Learning to optimize (L2O) is an emerging approach that leverages machine learning to develop optimization methods, aiming at reducing the laborious iterations of hand engineering.…
JFB: Jacobian-Free Backpropagation for Implicit Networks
Samy Wu Fung, Howard Heaton, Qiuwei Li +3
A promising trend in deep learning replaces traditional feedforward networks with implicit networks. Unlike traditional networks, implicit networks solve a fixed point equation to…
Wasserstein-based Projections with Applications to Inverse Problems
Howard Heaton, Samy Wu Fung, Alex Tong Lin +2
Inverse problems consist of recovering a signal from a collection of noisy measurements. These are typically cast as optimization problems, with classic approaches using a data fid…
Safeguarded Learned Convex Optimization
Howard Heaton, Xiaohan Chen, Zhangyang Wang +1
Applications abound in which optimization problems must be repeatedly solved, each time with new (but similar) data. Analytic optimization algorithms can be hand-designed to provab…
Asynchronous Sequential Inertial Iterations for Common Fixed Points Problems with an Application to Linear Systems
Howard Heaton, Yair Censor
The common fixed points problem requires finding a point in the intersection of fixed points sets of a finite collection of operators. Quickly solving problems of this sort is of g…
Derivative-free superiorization with component-wise perturbations
Yair Censor, Howard Heaton, Reinhard Schulte
Superiorization reduces, not necessarily minimizes, the value of a target function while seeking constraints-compatibility. This is done by taking a solely feasibility-seeking algo…