# Disciplined Geometric Programming

arXiv: https://arxiv.org/abs/1812.04074 · HTML: https://mlsanity.com/paper/1812.04074/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Dec 2018.

## Built on by (most cited first, 8 of 8)

- [A Symmetry-Aware Exploration of Bayesian Neural Network Posteriors](https://mlsanity.com/paper/2310.08287/) (2023)
- [On the convex formulations of robust Markov decision processes](https://mlsanity.com/paper/2209.10187/) (2022)
- [Disciplined Biconvex Programming](https://mlsanity.com/paper/2511.01813/) (2025)
- [Deep Incentive Design with Differentiable Equilibrium Blocks](https://mlsanity.com/paper/2603.07705/) (2026)
- [An Information-Geometric Approach to Artificial Curiosity](https://mlsanity.com/paper/2504.06355/) (2025)
- [Simulation-based Methods for Optimal Sampling Design in Systems Biology](https://mlsanity.com/paper/2511.07197/) (2025)
- [Optimizing Server Placement for Vertical Federated Learning in Dynamic Edge/Fog Networks](https://mlsanity.com/paper/2605.09813/) (2026)
- [Disciplined Bilevel Programming](https://mlsanity.com/paper/2609.00644/) (2026)

## Abstract (arXiv)

We introduce log-log convex programs, which are optimization problems with positive variables that become convex when the variables, objective functions, and constraint functions are replaced with their logs, which we refer to as a log-log transformation. This class of problems generalizes traditional geometric programming and generalized geometric programming, and it includes interesting problems involving nonnegative matrices. We give examples of log-log convex functions, some well-known and some less so, and we develop an analog of disciplined convex programming, which we call disciplined geometric programming. Disciplined geometric programming is a subclass of log-log convex programming generated by a composition rule and a set of functions with known curvature under the log-log transformation. Finally, we describe an implementation of disciplined geometric programming as a reduction in CVXPY 1.0.