# Uncertain random geometric programming problems

arXiv: https://arxiv.org/abs/2310.01848 · HTML: https://mlsanity.com/paper/2310.01848/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Oct 2023.

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

- [Reason, Reward, Refine: Step-Level Errors Corrections with Structured Feedback for Physics Reasoning in Small Language Models](https://mlsanity.com/paper/2607.05199/) (2026)

## Abstract (arXiv)

In this paper, we introduce a deterministic formulation for the geometric programming problem, wherein the coefficients are represented as independent linear-normal uncertain random variables. To address the challenges posed by this combination of uncertainty and randomness, we introduce the concept of an uncertain random variable and present a novel framework known as the linear-normal uncertain random variable. Our main focus in this work is the development of three distinct transformation techniques: the optimistic value criteria, pessimistic value criteria, and expected value criteria. These approaches allow us to convert a linear-normal uncertain random variable into a more manageable random variable. This transition facilitates the transformation from an uncertain random geometric programming problem to a stochastic geometric programming problem. Furthermore, we provide insights into an equivalent deterministic representation of the transformed geometric programming problem, enhancing the clarity and practicality of the optimization process. To demonstrate the effectiveness of our proposed approach, we present a numerical example.