Globalization of SQP-Methods in Control of the Instationary Navier-Stokes Equations

A numerically inexpensive globalization strategy of sequential quadratic programming methods (SQP-methods) for control of the instationary Navier Stokes equations is investigated. Based on the proper functional analytic setting a convergence analysis for the globalized method is given. It is argued that the a priori formidable SQP-step can be decomposed into linear primal and linear adjoint systems, which is amenable for existing CFL-software. A report on a numerical test demonstrates the feasibility of the approach.

[1]  F.-S. Kupfer,et al.  An Infinite-Dimensional Convergence Theory for Reduced SQP Methods in Hilbert Space , 1996, SIAM J. Optim..

[2]  M. Heinkenschloss.  Formulation and Analysis of a Sequential Quadratic Programming Method for the Optimal Dirichlet Boundary Control of Navier-Stokes Flow , 1998 .

[3]  Karl Kunisch,et al.  Second Order Methods for Optimal Control of Time-Dependent Fluid Flow , 2001, SIAM J. Control. Optim..

[4]  Ekkehard W. Sachs,et al.  Algorithmic methods in optimal control , 1981 .

[5]  Philip E. Gill,et al.  Practical optimization , 1981 .

[6]  M. Hinze.  Optimal and instantaneous control of the instationary Navier-Stokes equations , 2002 .

[7]  Omar Ghattas,et al.  Optimal Control of Two- and Three-Dimensional Incompressible Navier-Stokes Flows , 1997 .

[8]  R. Temam,et al.  On some control problems in fluid mechanics , 1990 .

[9]  E. Bänsch.  An adaptive finite-element strategy for the three-dimensional time-dependent Navier-Stokes equations , 1991 .

[10]  Werner C. Rheinboldt,et al.  Methods for Solving Systems of Nonlinear Equations: Second Edition , 1998 .

[11]  M. Hintermueller.  On a globalized augmented Lagrangian SQP-algorithm for nonlinear optimal control problems with box constraints , 2001 .

[12]  Werner C. Rheinboldt,et al.  Methods for solving systems of nonlinear equations , 1987 .

[13]  K. Schittkowski,et al.  NONLINEAR PROGRAMMING , 2022 .

[14]  R. Glowinski,et al.  Incompressible Computational Fluid Dynamics: On Some Finite Element Methods for the Numerical Simulation of Incompressible Viscous Flow , 1993 .

[15]  C. Kelley.  Iterative Methods for Linear and Nonlinear Equations , 1987 .

[16]  Hantaek Bae.  Navier-Stokes equations , 1992 .

[17]  P. Hood,et al.  A numerical solution of the Navier-Stokes equations using the finite element technique , 1973 .

[18]  M. J. D. Powell,et al.  Variable Metric Methods for Constrained Optimization , 1982, ISMP.