SC '05 Proceedings of the 2005 ACM/IEEE conference on Supercomputing
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Proceedings of the 2009 ACM symposium on Applied Computing
Large-Scale Scientific Computing
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Multilevel Algorithms for Large-Scale Interior Point Methods
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Analysis of Block Parareal Preconditioners for Parabolic Optimal Control Problems
SIAM Journal on Scientific Computing
An Interior-Point Algorithm for Large-Scale Nonlinear Optimization with Inexact Step Computations
SIAM Journal on Scientific Computing
A Robust Multigrid Method for Elliptic Optimal Control Problems
SIAM Journal on Numerical Analysis
Inversion of airborne contaminants in a regional model
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part III
Domain decomposition methods for PDE constrained optimization problems
VECPAR'04 Proceedings of the 6th international conference on High Performance Computing for Computational Science
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In part I of this article, we proposed a Lagrange--Newton--Krylov--Schur (LNKS) method for the solution of optimization problems that are constrained by partial differential equations. LNKS uses Krylov iterations to solve the linearized Karush--Kuhn--Tucker system of optimality conditions in the full space of states, adjoints, and decision variables, but invokes a preconditioner inspired by reduced space sequential quadratic programming (SQP) methods. The discussion in part I focused on the (inner, linear) Krylov solver and preconditioner. In part II, we discuss the (outer, nonlinear) Lagrange--Newton solver and address globalization, robustness, and efficiency issues, including line search methods, safeguarding Newton with quasi-Newton steps, parameter continuation, and inexact Newton ideas. We test the full LNKS method on several large-scale three-dimensional configurations of a problem of optimal boundary control of incompressible Navier--Stokes flow with a dissipation objective functional. Results of numerical experiments on up to 256 Cray T3E-900 processors demonstrate very good scalability of the new method. Moreover, LNKS is an order of magnitude faster than quasi-Newton reduced SQP, and we are able to solve previously intractable problems of up to 800,000 state and 5,000 decision variables at about 5 times the cost of a single forward flow solution.