# Accelerated First-Order Methods for Hyperbolic Programming

arXiv: https://arxiv.org/abs/1512.07569 · HTML: https://mlsanity.com/paper/1512.07569/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Dec 2015.

## Built on by (most cited first, 3 of 3)

- [Restarts subject to approximate sharpness: A parameter-free and optimal scheme for first-order methods](https://mlsanity.com/paper/2301.02268/) (2023)
- [Gauges and Accelerated Optimization over Smooth and/or Strongly Convex Sets](https://mlsanity.com/paper/2303.05037/) (2023)
- [An Elementary Proof of the Near Optimality of LogSumExp Smoothing](https://mlsanity.com/paper/2512.10825/) (2025)

## Abstract (arXiv)

A framework is developed for applying accelerated methods to general hyperbolic programming, including linear, second-order cone, and semidefinite programming as special cases. The approach replaces a hyperbolic program with a convex optimization problem whose smooth objective function is explicit, and for which the only constraints are linear equations (one more linear equation than for the original problem). Virtually any first-order method can be applied. Iteration bounds for a representative accelerated method are derived.