Learning Parametric Convex Functions

Maximilian Schaller; Alberto Bemporad; Stephen Boyd

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arXiv · 2506.04183

Learning Parametric Convex Functions

Maximilian Schaller·Alberto Bemporad·Stephen Boyd

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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.

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Maximilian Schaller, Alberto Bemporad, Stephen Boyd. 2025-06-04. Learning Parametric Convex Functions. https://arxiv.org/abs/2506.04183

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