# Disjunctive cuts in Mixed-Integer Conic Optimization

arXiv: https://arxiv.org/abs/1912.03166 · HTML: https://mlsanity.com/paper/1912.03166/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Dec 2019.

## Built on by (most cited first, 1 of 1)

- [Differentiable Cutting-plane Layers for Mixed-integer Linear Optimization](https://mlsanity.com/paper/2311.03350/) (2023)

## Abstract (arXiv)

This paper studies disjunctive cutting planes in Mixed-Integer Conic Programming. Building on conic duality, we formulate a cut-generating conic program for separating disjunctive cuts, and investigate the impact of the normalization condition on its resolution. In particular, we show that a careful selection of normalization guarantees its solvability and conic strong duality. Then, we highlight the shortcomings of separating conic-infeasible points in an outer-approximation context, and propose conic extensions to the classical lifting and monoidal strengthening procedures. Finally, we assess the computational behavior of various normalization conditions in terms of gap closed, computing time and cut sparsity. In the process, we show that our approach is competitive with the internal lift-and-project cuts of a state-of-the-art solver.