# Sequential Quadratic Optimization for Stochastic Optimization with Deterministic Nonlinear Inequality and Equality Constraints

## TL;DR

This paper introduces a sequential quadratic optimization algorithm designed for stochastic problems with nonlinear constraints, where only stochastic gradient estimates are available for the objective, and provides convergence guarantees under mild assumptions.

## Contribution

It proposes a novel algorithm for stochastic constrained optimization that works with only stochastic gradient estimates and proves its convergence under loose assumptions.

## Key findings

- Algorithm outperforms alternative methods with more accurate gradient estimates
- Convergence guarantees are established under unbiased gradient estimates
- Numerical experiments demonstrate practical effectiveness

## Abstract

A sequential quadratic optimization algorithm for minimizing an objective function defined by an expectation subject to nonlinear inequality and equality constraints is proposed, analyzed, and tested. The context of interest is when it is tractable to evaluate constraint function and derivative values in each iteration, but it is intractable to evaluate the objective function or its derivatives in any iteration, and instead an algorithm can only make use of stochastic objective gradient estimates. Under loose assumptions, including that the gradient estimates are unbiased, the algorithm is proved to possess convergence guarantees in expectation. The results of numerical experiments are presented to demonstrate that the proposed algorithm can outperform an alternative approach that relies on the ability to compute more accurate gradient estimates.