# An adaptive discretization method solving semi-infinite optimization problems with quadratic rate of convergence

arXiv: https://arxiv.org/abs/1910.13798 · HTML: https://mlsanity.com/paper/1910.13798/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2019.

## 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)

Semi-infinite programming can be used to model a large variety of complex optimization problems. The simple description of such problems comes at a price: semi-infinite problems are often harder to solve than finite nonlinear problems. In this paper we combine a classical adaptive discretization method developed by Blankenship and Falk and techniques regarding a semi-infinite optimization problem as a bi-level optimization problem. We develop a new adaptive discretization method which combines the advantages of both techniques and exhibits a quadratic rate of convergence. We further show that a limit of the iterates is a stationary point, if the iterates are stationary points of the approximate problems.