Michael Hinze, K. Kunisch:

Second Order Methods for Optimal Control of Time -- Dependent Fluid Flow

Second order methods for open loop optimal control problems governed by the two-dimensional instationary Navier-Stokes equations are investigated. Optimality systems based on a Lagrangian formulation and adjoint equations are derived. The Newton and quasi-Newton methods as well as various variants of SQP-methods are developed for applications to optimal flow control and their complexity in terms of system solves is discussed. Local convergence and rate of convergence are proved. A numerical example illustrates the feasibility of solving optimal control problems for two-dimensional instationary Navier-Stokes equations by second order numerical methods in a standard workstation environment. Previously such problems were solved by gradient type methods.

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