A Sequential Quadratic Programming Method for Optimization with Stochastic Objective Functions, Deterministic Inequality Constraints and Robust Subproblems

TL;DR

This paper introduces a robust sequential quadratic programming method tailored for constrained optimization problems involving stochastic objective functions and deterministic constraints, ensuring convergence to optimality under certain conditions.

Contribution

It generalizes existing SQP methods to stochastic objectives with a stochastic line search for global convergence guarantees.

Findings

Sequences converge almost surely to a KKT point.

The method demonstrates promising numerical results.

Theoretical convergence is established under specific constraint qualifications.

Abstract

In this paper, a robust sequential quadratic programming method for constrained optimization is generalized to problem with an {expectation} objective function {and} deterministic equality and inequality constraints. A stochastic line search scheme is employed to globalize the steps. {We show theoretically that sequences generated by the algorithm converge almost surely to a Karush-Kuhn-Tucker point under the assumption of the extended Mangasarian-Fromovitz constraint qualification}. Encouraging numerical results are reported.