# Active-set prediction for interior point methods using controlled perturbations

arXiv: https://arxiv.org/abs/1404.6770 · HTML: https://mlsanity.com/paper/1404.6770/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Apr 2014.

## Built on by (most cited first, 2 of 2)

- [Inequality Constrained Stochastic Nonlinear Optimization via Active-Set Sequential Quadratic Programming](https://mlsanity.com/paper/2109.11502/) (2021)
- [Differentiation Through Black-Box Quadratic Programming Solvers](https://mlsanity.com/paper/2410.06324/) (2024)

## Abstract (arXiv)

We propose the use of controlled perturbations to address the challenging question of optimal active-set prediction for interior point methods. Namely, in the context of linear programming, we consider perturbing the inequality constraints/bounds so as to enlarge the feasible set. We show that if the perturbations are chosen appropriately, the solution of the original problem lies on or close to the central path of the perturbed problem. We also find that a primal-dual path-following algorithm applied to the perturbed problem is able to accurately predict the optimal active set of the original problem when the duality gap for the perturbed problem is not too small; furthermore, depending on problem conditioning, this prediction can happen sooner than predicting the active set for the perturbed problem or when the original one is solved. Encouraging preliminary numerical experience is reported when comparing activity prediction for the perturbed and unperturbed problem formulations.