On the effects of scaling on the performance of Ipopt

TL;DR

This paper investigates how different scaling algorithms impact the performance of the Ipopt nonlinear solver when using a new linear solver, HSL_MA97, across a broad set of test problems.

Contribution

It introduces the use of various scaling algorithms within Ipopt with HSL_MA97 and evaluates their effects on performance using extensive benchmark problems.

Findings

Scaling algorithms significantly affect solver speed and robustness.

Certain scaling methods improve solution accuracy.

Performance varies depending on problem characteristics.

Abstract

The open-source nonlinear solver Ipopt (https://projects.coin-or.org/Ipopt) is a widely-used software package for the solution of large-scale non-linear optimization problems. At its heart, it employs a third-party linear solver to solve a series of sparse symmetric indefinite systems. The speed, accuracy and robustness of the chosen linear solver is critical to the overall performance of Ipopt. In some instances, it can be beneficial to scale the linear system before it is solved. In this paper, different scaling algorithms are employed within Ipopt with a new linear solver HSL_MA97 from the HSL mathematical software library (http://www.hsl.rl.ac.uk). An extensive collection of problems from the CUTEr test set (http://www.cuter.rl.ac.uk) is used to illustrate the effects of scaling.