NOWPAC: A provably convergent derivative-free nonlinear optimizer with path-augmented constraints (1403.1931v3)

Abstract: This paper proposes the algorithm NOWPAC (Nonlinear Optimization With Path-Augmented Constraints) for nonlinear constrained derivative-free optimization. The algorithm uses a trust region framework based on fully linear models for the objective function and the constraints. A new constraint-handling scheme based on an inner boundary path allows for the computation of feasible trial steps using models for the constraints. We prove that the iterates computed by NOWPAC converge to a first-order critical point. We also discuss the convergence of NOWPAC in situations where evaluations of the objective function or the constraints are inexact, e.g., corrupted by numerical errors. We determine a rate of decay that the magnitude of these numerical errors must satisfy, while approaching the critical point, to guarantee convergence. In settings where adjusting the accuracy of the objective or constraint evaluations is not possible, as is often the case in practical applications, we introduce an error indicator to detect these regimes and prevent deterioration of the optimization results.