Abstract
The problem of constrained optimization via the gradient-based discrete adjoint steepest descent method is studied under the assumption that the constraint equations are solved inexactly. Error propagation from the constraint equations to the gradient is studied analytically, as is the convergence rate of the inexactly constrained algorithm as it relates to the exact algorithm. A method is developed for adapting the residual tolerance to which the constraint equations are solved. The adaptive tolerance method is applied to two simple test cases to demonstrate the potential gains in computational efficiency.
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The authors gratefully acknowledge funding from the National Sciences and Engineering Research Council of Canada (NSERC) as well as Bombardier Aerospace.
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Brown, D.A., Nadarajah, S. Inexactly constrained discrete adjoint approach for steepest descent-based optimization algorithms. Numer Algor 78, 983–1000 (2018). https://doi.org/10.1007/s11075-017-0409-7
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DOI: https://doi.org/10.1007/s11075-017-0409-7