Design and implementation of a modular interior-point solver for linear optimization

TL;DR

This paper presents Tulip, an open-source Julia-based interior-point solver for linear optimization that handles unbounded and infeasible problems, with specialized routines for structured problems and extended precision capabilities.

Contribution

The paper introduces Tulip, a modular interior-point solver with a flexible framework, specialized routines for structured problems, and demonstrated superior performance on large-scale instances.

Findings

Tulip is competitive with existing open-source solvers.

Specialized routines achieve tenfold speedup on large, dense problems.

Tulip effectively uses extended arithmetic precision.

Abstract

This paper introduces the algorithmic design and implementation of Tulip, an open-source interior-point solver for linear optimization. It implements a regularized homogeneous interior-point algorithm with multiple centrality corrections, and therefore handles unbounded and infeasible problems. The solver is written in Julia, thus allowing for a flexible and efficient implementation: Tulip's algorithmic framework is fully disentangled from linear algebra implementations and from a model's arithmetic. In particular, this allows to seamlessly integrate specialized routines for structured problems. Extensive computational results are reported. We find that Tulip is competitive with open-source interior-point solvers on the H. Mittelmann's benchmark of barrier linear programming solvers. Furthermore, we design specialized linear algebra routines for structured master problems in the context of Dantzig-Wolfe decomposition. These routines yield a tenfold speedup on large and dense instances that arise in power systems operation and two-stage stochastic programming, thereby outperforming state-of-the-art commercial interior point method solvers. Finally, we illustrate Tulip's ability to use different levels of arithmetic precision by solving problems in extended precision.