English

Learning Parametric Convex Functions

Optimization and Control 2025-06-05 v1

Abstract

A parametrized convex function depends on a variable and a parameter, and is convex in the variable for any valid value of the parameter. Such functions can be used to specify parametrized convex optimization problems, i.e., a convex optimization family, in domain specific languages for convex optimization. In this paper we address the problem of fitting a parametrized convex function that is compatible with disciplined programming, to some given data. This allows us to fit a function arising in a convex optimization formulation directly to observed or simulated data. We demonstrate our open-source implementation on several examples, ranging from illustrative to practical.

Keywords

Cite

@article{arxiv.2506.04183,
  title  = {Learning Parametric Convex Functions},
  author = {Maximilian Schaller and Alberto Bemporad and Stephen Boyd},
  journal= {arXiv preprint arXiv:2506.04183},
  year   = {2025}
}