Augmenting the one-shot framework by additional constraints

Abstract

The (multistep) one-shot method for design optimization problems has been successfully implemented for various applications. To this end, a slowly convergent primal fixed-point iteration of the state equation is augmented by an adjoint iteration and a corresponding preconditioned design update. In this paper we present a modification of the method that allows for additional equality constraints besides the usual state equation. A retardation analysis and the local convergence of the method in terms of necessary and sufficient conditions are given, which depend on key characteristics of the underlying problem and the quality of the utilized preconditioner.

Keywords:

• nonlinear optimization
• automatic differentiation
• piggyback
• one-shot method
• constraints
• eigenvalue analysis

AMS Subject Classification:

• 49M05
• 65F08
• 65F15
• 90M50
• 90C30

Acknowledgements

Government license section: The submitted manuscript has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (‘Argonne’). Argonne, a US Department of Energy Office of Science laboratory, is operated under Contract No. DE-AC02-06CH11357. The US Government retains for itself, and others acting on its behalf, a paid-up non-exclusive, irrevocable worldwide license in said article to reproduce, prepare derivative works, distribute copies to the public, and perform publicly and display publicly, by or on behalf of the Government.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1. The derivatives will be denoted with subscripts, and the argument is skipped whenever it is unambiguous where the derivative is evaluated; for example, , , and denote the Jacobians of G, g, and the gradient of f with respect to y, respectively.

Additional information

Funding

This material is based upon work partly supported by the U.S. Department of Energy, Office of Science [contract number DE-AC02-06CH11357].