One-shot approaches to design optimzation. (English) Zbl 1327.90300
Leugering, Günter (ed.) et al., Trends in PDE constrained optimization. Cham: Birkhäuser/Springer (ISBN 978-3-319-05082-9/hbk; 978-3-319-05083-6/ebook). ISNM. International Series of Numerical Mathematics 165, 43-66 (2014).
Summary: The paper describes general methodologies for the solution of design optimization problems. In particular we outline the close relations between a fixed point solver based piggy back approach and a Reduced SQP method in Jacobi and Seidel variants. The convergence rate and general efficacy is shown to be strongly dependent on the characteristics of the state equation and the objective function. In the QP scenario where the state equation is linear and the objective quadratic, finite termination in two steps is obtained by the Seidel variant with Newton state solver and perfect design space preconditioning. More generally, it is shown that the retardation factor between simulation and optimization is bounded below by 2 with the difference depending on a cross-term representing the total sensitivity of the adjoint equation with respect to the design.
For the entire collection see [Zbl 1306.49001].
For the entire collection see [Zbl 1306.49001].
MSC:
| 90C30 | Nonlinear programming |
| 68U20 | Simulation (MSC2010) |
| 35Q68 | PDEs in connection with computer science |
| 35Q90 | PDEs in connection with mathematical programming |
| 35Q93 | PDEs in connection with control and optimization |
Keywords:
simulation; optimization; PDE; automatic differentiation; fixed-point solver; retardation factor; convergence; numericsReferences:
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