lpviz: Interactive Linear Programming Visualization

2026-04-30

AI Summary

This work addresses the lack of intuitive, interactive tools for gaining deep insight into the behavior of linear programming solvers and their responses to changes in feasible regions and objective functions. To bridge this gap, the authors present a browser-based interactive visualization system that uniquely enables users to graphically edit linear programming problems in real time and simultaneously compare the solution trajectories of multiple mainstream algorithms—such as the simplex and interior-point methods. The system visualizes solver iterations and internal states through 3D height-mapped representations of the optimization landscape. Built on web technologies, the tool is open-source, cross-platform, and has been validated in both educational and research settings, demonstrably enhancing users’ understanding of algorithmic characteristics and parameter sensitivities.

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 .

Problem

• linear programming
• algorithm visualization
• solver behavior
• interactive learning
• optimization

Innovation

• interactive visualization
• linear programming
• algorithm comparison
• 3D solver metadata
• browser-based tool