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New Results for the Handling of Additional Equality Constraints in One-Shot Optimization

Research paper by Andrea Walther, Lisa Kusch, Nicolas R. Gauger

Indexed on: 07 Sep '18Published on: 06 Sep '18Published in: Vietnam Journal of Mathematics



Abstract

The one-shot approach is often applied for design optimization tasks involving a slowly converging Newton-like solver for the underlying partial differential equations. The state solver is augmented with an adjoint solver to obtain reduced derivatives for an optimization step. The idea of the one-shot approach is to simultaneously pursue state and adjoint feasibility as well as optimality by using a suitable design space preconditioner. In various applications, further equality constraints additional to the partial differential equations describing the state are required. The one-shot approach can be extended to deal with additional equality constraints by introducing an additional update formula for the corresponding constraint multipliers. The choice of a suitable preconditioner for the design update as well as for the constraint multiplier update is important to achieve bounded retardation. We derive conditions for the preconditioners of the extended one-shot approach and propose a suitable preconditioner for the multiplier updates for the additional constraints.