# Proximal-gradient algorithms for fractional programming

arXiv: https://arxiv.org/abs/1601.08166 · HTML: https://mlsanity.com/paper/1601.08166/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jan 2016.

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

- [Coordinate Descent Methods for Fractional Minimization](https://mlsanity.com/paper/2201.12691/) (2022)

## Abstract (arXiv)

In this paper we propose two proximal gradient algorithms for fractional programming problems in real Hilbert spaces, where the numerator is a proper, convex and lower semicontinuous function and the denominator is a smooth function, either concave or convex. In the iterative schemes, we perform a proximal step with respect to the nonsmooth numerator and a gradient step with respect to the smooth denominator. The algorithm in case of a concave denominator has the particularity that it generates sequences which approach both the (global) optimal solutions set and the optimal objective value of the underlying fractional programming problem. In case of a convex denominator the numerical scheme approaches the set of critical points of the objective function, provided the latter satisfies the Kurdyka-Lojasiewicz property.