# Semidefinite Programming For Chance Constrained Optimization Over Semialgebraic Sets

arXiv: https://arxiv.org/abs/1402.6382 · HTML: https://mlsanity.com/paper/1402.6382/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2014.

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

- [Fast nonlinear risk assessment for autonomous vehicles using learned conditional probabilistic models of agent futures](https://mlsanity.com/paper/2109.09975/) (2021)

## Abstract (arXiv)

In this paper, "chance optimization" problems are introduced, where one aims at maximizing the probability of a set defined by polynomial inequalities. These problems are, in general, nonconvex and computationally hard. With the objective of developing systematic numerical procedures to solve such problems, a sequence of convex relaxations based on the theory of measures and moments is provided, whose sequence of optimal values is shown to converge to the optimal value of the original problem. Indeed, we provide a sequence of semidefinite programs of increasing dimension which can arbitrarily approximate the solution of the original problem. To be able to efficiently solve the resulting large-scale semidefinite relaxations, a first-order augmented Lagrangian algorithm is implemented. Numerical examples are presented to illustrate the computational performance of the proposed approach.