# Optimality conditions in control problems with random state constraints in probabilistic or almost-sure form

arXiv: https://arxiv.org/abs/2306.03965 · HTML: https://mlsanity.com/paper/2306.03965/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2023.

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

- [Infinite-dimensional spherical-radial decomposition for probabilistic functions, with application to constrained optimal control and Gaussian process regression](https://mlsanity.com/paper/2603.19907/) (2026)

## Abstract (arXiv)

In this paper, we discuss optimality conditions for optimization problems involving random state constraints, which are modeled in probabilistic or almost sure form. While the latter can be understood as the limiting case of the former, the derivation of optimality conditions requires substantially different approaches. We apply them to a linear elliptic partial differential equation (PDE) with random inputs. In the probabilistic case, we rely on the spherical-radial decomposition of Gaussian random vectors in order to formulate fully explicit optimality conditions involving a spherical integral. In the almost sure case, we derive optimality conditions and compare them to a model based on robust constraints with respect to the (compact) support of the given distribution.