# An Inexact Primal-Dual Algorithm for Semi-Infinite Programming

arXiv: https://arxiv.org/abs/1803.10898 · HTML: https://mlsanity.com/paper/1803.10898/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Mar 2018.

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

- [Exchange Policy Optimization Algorithm for Semi-Infinite Safe Reinforcement Learning](https://mlsanity.com/paper/2511.04147/) (2025)

## Abstract (arXiv)

This paper considers an inexact primal-dual algorithm for semi-infinite programming (SIP) for which it provides general error bounds. To implement the dual variable update, we create a new prox function for nonnegative measures which turns out to be a generalization of the Kullback-Leibler divergence for probability distributions. We show that under suitable conditions on the error, this algorithm achieves an O(1/√K) rate of convergence in terms of the optimality gap and constraint violation. We then use our general error bounds to analyze the convergence and sample complexity of a specific primal-dual SIP algorithm based on Monte Carlo integration. Finally, we provide numerical experiments to demonstrate the performance of our algorithm.