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

Abstract

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.