lpviz: Interactive Linear Programming Visualization

TL;DR

lpviz is an interactive, browser-based visualization tool for linear programming that helps users understand solver behavior and compare different algorithms through intuitive graphical interfaces.

Contribution

It introduces a novel interactive visualization platform for linear programming that supports multiple algorithms and provides insights into solver metadata.

Findings

Enables direct manipulation of feasible regions and objective vectors.

Supports comparison of Simplex, Interior-Point, Primal-Dual Hybrid Gradient, and Central Path algorithms.

Provides 3D visualization of solver metadata like KKT residuals.

Abstract

This paper presents lpviz, a browser-based visualization tool for linear programming. lpviz is deeply interactive, offering an intuitive interface where users can directly draw and edit the feasible region and objective vector, without requiring cumbersome manipulation of raw numerical coefficients. lpviz lets users compare the behavior of several classes of linear programming algorithms, namely Simplex, Interior-Point, Primal-Dual Hybrid Gradient, and Central Path. In the 3D mode, lpviz places iterates at heights corresponding to important solver metadata such as complementarity gap or KKT residual, helping users gain further insight into algorithm behavior beyond the primal iterates alone. lpviz has been used in both research and classroom settings, to help develop intuition for the strengths and weaknesses of different solvers and the impact of solver settings on convergence behavior. lpviz is open-source, permissively licensed, and freely available on any device with a web browser at https://lpviz.net .