Adaptive Sampling Trust Region Optimization for Derivative-free Stochastic Functions and Deterministic Equality Constraints

We study optimization problems with noisy zeroth-order objective observations and deterministic nonlinear equality constraints with available derivatives. We propose a constrained variant of the adaptive-sampling trust-region derivative-free optimization algorithm—ASTRO-DF. The method builds quadratic local models from estimated objective values at interpolation points within a moving trust region and promotes feasibility through a Byrd–Omojokun composite-step based on linearized constraints, following an SQP-like framework. We prove almost sure convergence using a new constrained criticality test and present numerical results on an equality-constrained stochastic activity network problem.

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