# Approximate solutions of convex semi-infinite optimization problems in finitely many iterations

arXiv: https://arxiv.org/abs/2105.08417 · HTML: https://mlsanity.com/paper/2105.08417/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2021.

## Built on by (most cited first, 2 of 2)

- [Capturing and incorporating expert knowledge into machine learning models for quality prediction in manufacturing](https://mlsanity.com/paper/2202.02003/) (2022)
- [Accelerating nanodrug development in continuous flow systems using informed prediction models based on low-cost surrogate nanoparticles](https://mlsanity.com/paper/2608.05761/) (2026)

## Abstract (arXiv)

We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of the considered optimization problem. Compared to the existing finitely feasible algorithms for general semi-infinite optimization problems, our algorithms work with considerably smaller discretizations and are thus computationally favorable. Also, our algorithms terminate at approximate solutions of arbitrary precision, while for general semi-infinite optimization problems the best possible approximate-solution precision can be arbitrarily bad. All occurring finite optimization subproblems in our algorithms have to be solved only approximately, and continuity is the only regularity assumption on our objective and constraint functions. Applications to parametric and non-parametric regression problems under shape constraints are discussed.