# The self-concordant perceptron is efficient on a sub-family feasibility instances

## TL;DR

This paper introduces a self-concordant perceptron algorithm that efficiently solves a specific sub-family of strict linear feasibility problems using an interior point approach, offering precise complexity analysis.

## Contribution

It presents a novel perceptron-based method leveraging interior point techniques for strict linear feasibility, with detailed complexity characterization on certain problem sub-families.

## Key findings

- Algorithm matches state-of-the-art linear programming complexity
- Binary complexity is low on a specific sub-family of instances
- Provides a more precise complexity analysis for the problem

## Abstract

Strict linear feasibility or linear separation is usually tackled using efficient approximation/stochastic algorithms (that may even run in sub-linear times in expectation). However, today state of the art for solving exactly/deterministically such instances is to cast them as a linear programming instances. Inversely, this paper introduces a self-concordant perceptron algorithm which tackles directly strict linear feasibility with interior point paradigm. This algorithm has the same worse times complexity than state of the art linear programming algorithms but it complexity can be characterized more precisely eventually proving that it binary complexity is low on a sub-family of linear feasibility.