Worst-case complexity of an SQP method for nonlinear equality constrained stochastic optimization

• 成果类型: Article
• 署名作者: Curtis, Frank E.; O'Neill, Michael J.; Robinson, Daniel P.
• 署名单位: Lehigh University; University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-023-01981-1
• 发表日期: 2024
• 页码: 431-483
• 关键词: Nonconvex optimization; algorithm

摘要

A worst-case complexity bound is proved for a sequential quadratic optimization (commonly known as SQP) algorithm that has been designed for solving optimization problems involving a stochastic objective function and deterministic nonlinear equality constraints. Barring additional terms that arise due to the adaptivity of the monotonically nonincreasing merit parameter sequence, the proved complexity bound is comparable to that known for the stochastic gradient algorithm for unconstrained nonconvex optimization. The overall complexity bound, which accounts for the adaptivity of the merit parameter sequence, shows that a result comparable to the unconstrained setting (with additional logarithmic factors) holds with high probability.