A Trust-Region Algorithm for Noisy Equality Constrained Optimization

TL;DR

This paper develops a modified trust-region algorithm based on Byrd-Omojokun for solving equality constrained optimization problems with noisy function and gradient evaluations, enhancing robustness and convergence analysis.

Contribution

It introduces a new noise-aware acceptance and update criterion for the trust region, extending the BO method to noisy environments with convergence guarantees.

Findings

Algorithm converges to stationary points under noise conditions

Numerical tests demonstrate practical effectiveness

Enhanced robustness in rank-deficient constraint scenarios

Abstract

This paper introduces a modified Byrd-Omojokun (BO) trust region algorithm to address the challenges posed by noisy function and gradient evaluations. The original BO method was designed to solve equality constrained problems and it forms the backbone of some interior point methods for general large-scale constrained optimization. A key strength of the BO method is its robustness in handling problems with rank-deficient constraint Jacobians. The algorithm proposed in this paper introduces a new criterion for accepting a step and for updating the trust region that makes use of an estimate in the noise in the problem. The analysis presented here gives conditions under which the iterates converge to regions of stationary points of the problem, determined by the level of noise. This analysis is more complex than for line search methods because the trust region carries (noisy) information from previous iterates. Numerical tests illustrate the practical performance of the algorithm.