A Noise Tolerant SQP Algorithm for Inequality Constrained Optimization

TL;DR

This paper introduces a noise-tolerant SQP algorithm for inequality constrained optimization that maintains convergence and accuracy despite bounded noise in function and derivative evaluations.

Contribution

It presents a robust line search SQP method with relaxations and noise-aware quasi-Newton updates, addressing noise in both objective and constraint evaluations.

Findings

The algorithm achieves accuracy proportional to the noise level.

Numerical experiments confirm robustness to bounded noise.

Theoretical analysis supports convergence despite noise presence.

Abstract

We propose a sequential quadratic programming (SQP) algorithm for inequality constrained optimization that is robust to the presence of bounded noise in function and derivative evaluations. We cover the case where constraint evaluations contain noise as well as the objective. The proposed algorithm is a line search SQP method with relaxations to deal with noise. We study the effect of noise on the global convergence behavior of the algorithm. We implement the algorithm with noise-aware quasi-Newton updates, and numerically observe that the algorithm can achieve accuracy proportional to the noise level and problem-dependent parameters, as suggested by the theory.