Stochastic-objective extension of the primal-dual Newton-MR method

Develop an extension of the primal-dual Newton-MR algorithm and its convergence analysis to the stochastic-objective setting, where objective information is obtained from noisy or stochastic oracles.

Background

The paper develops and analyzes a deterministic inexact primal-dual Newton method for nonconvex equality-constrained optimization. Its convergence guarantees rely on deterministic evaluations of the objective, constraints, gradients, Jacobian, and Hessian-vector products.

The paper notes that recent sequential quadratic programming research has begun addressing stochastic objectives and corresponding complexity guarantees. Extending the proposed primal-dual Newton-MR framework to this setting is explicitly left for future work, with the goal of broadening its applicability to large-scale problems in which objective information is noisy or sampled.