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math.OC2026
An Adaptive Augmented Lagrangian Method for Deterministic and Stochastic Nonconvex Optimization
Tianzhu Liu, Michael J. O'Neill
We present an inexact Augmented Lagrangian algorithm for solving nonlinear, non-convex optimization problems. Unlike most recently proposed Augmented Lagrangian methods with worst-…
math.OC2026
Complexity of an inexact stochastic SQP algorithm for equality constrained optimization
Michael J. O'Neill, Aoji Tang
In this paper, we consider nonlinear optimization problems with a stochastic objective function and deterministic equality constraints. We propose an inexact two-stepsize stochasti…
math.OC2026
A Sequential Cubic Programming Method with Second-Order Complexity Guarantees for Equality Constrained Optimization
Nikos Dimou, Michael J. O'Neill
We develop a new method for equality constrained optimization problems based on a sequential cubic programming framework. Each iteration utilizes a step decomposition based on the…