Solving Noisy, Large-Scale Fixed-Point Problems and Systems of Nonlinear Equations
Transportation Science
SNOBFIT -- Stable Noisy Optimization by Branch and Fit
ACM Transactions on Mathematical Software (TOMS)
Journal of Global Optimization
Algorithm 909: NOMAD: Nonlinear Optimization with the MADS Algorithm
ACM Transactions on Mathematical Software (TOMS)
A global optimization method for the design of space trajectories
Computational Optimization and Applications
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In this paper we show how the implicit filtering algorithm can be coupled with the BFGS quasi-Newton update to obtain a superlinearly convergent iteration if the noise in the objective function decays sufficiently rapidly as the optimal point is approached. In this way we give insight into the observations of good performance in practice of quasi-Newton methods when they are coupled with implicit filtering. We also report on numerical experiments that show how an implementation of implicit filtering that exploits these new results can improve the performance of the algorithm.