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This paper proposes the algorithm NOWPAC (Nonlinear Optimization WithPath-Augmented Constraints) for nonlinear constrained derivative-freeoptimization. The algorithm uses a trust region framework based on fully linearmodels for the objective function and the constraints. A newconstraint-handling scheme based on an inner boundary path allows for thecomputation of feasible trial steps using models for the constraints. We provethat the iterates computed by NOWPAC converge to a first-order critical point.We also discuss the convergence of NOWPAC in situations where evaluations ofthe objective function or the constraints are inexact, e.g., corrupted bynumerical errors. We determine a rate of decay that the magnitude of thesenumerical errors must satisfy, while approaching the critical point, toguarantee convergence. In settings where adjusting the accuracy of theobjective or constraint evaluations is not possible, as is often the case inpractical applications, we introduce an error indicator to detect these regimesand prevent deterioration of the optimization results.

NOWPAC: A provably convergent derivative-free nonlinear optimizer with path-augmented constraints