# Stochastic Polynomial Optimization

## TL;DR

This paper introduces a stochastic polynomial optimization framework using sample averages and Moment-SOS relaxations, analyzing its properties and demonstrating effectiveness through numerical experiments.

## Contribution

It presents a novel approach combining sample average approximation with Moment-SOS relaxations for stochastic polynomial optimization.

## Key findings

- Effective solution method demonstrated via numerical experiments
- Properties of the proposed optimization and relaxations analyzed
- Sample average approach integrated with Moment-SOS relaxations

## Abstract

This paper studies stochastic optimization problems with polynomials. We propose an optimization model with sample averages and perturbations. The Lasserre type Moment-SOS relaxations are used to solve the sample average optimization. Properties of the optimization and its relaxations are studied. Numerical experiments are presented.