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

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 d...

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Bibliographic Details
Published in:Mathematical programming Vol. 205; no. 1-2; pp. 431 - 483
Main Authors: Curtis, Frank E., O’Neill, Michael J., Robinson, Daniel P.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2024
Springer
Subjects:
Algorithms
Analysis
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Full Length Paper
Management science
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Methods
Numerical Analysis
Theoretical
68Q25
68W40
65K05
Nonlinear optimization
90C06
Sequential quadratic optimization
65Y20
Worst-case complexity
90C30
90C55
49M37
Stochastic optimization
62L20
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary: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.
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-023-01981-1