Representations of quasi-Newton matrices and their use in limited memory methods
Mathematical Programming: Series A and B
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
Aerodynamic shape optimization using simultaneous pseudo-timestepping
Journal of Computational Physics
Reduced quasi-Newton method for simultaneous design and optimization
Computational Optimization and Applications
The Art of Differentiating Computer Programs: An Introduction to Algorithmic Differentiation
The Art of Differentiating Computer Programs: An Introduction to Algorithmic Differentiation
One-shot methods in function space for PDE-constrained optimal control problems
Optimization Methods & Software - Special issue: the 8th International Conference on Numerical Optimization and Numerical Linear Algebra, November 7-11, 2011, Xiamen, China
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Many researchers have used Oneshot optimization methods based on user-specified primal state iterations, the corresponding adjoint iterations, and appropriately preconditioned design steps. Our goal here is to develop heuristics for sequencing these three subtasks, in order to optimize the convergence rate of the resulting coupled iteration cycle. A key ingredient is the preconditioning in the design step by a BFGS approximation of the projected Hessian. We provide a hard bound on the spectral radius of the coupled iteration cycle at local minima satisfying second order sufficiency conditions. Finally, we show how certain problem specific parameters can be estimated by local samples and be used to steer the whole process adaptively. We present limited numerical results that confirm the theoretical analysis.