Reduced quasi-Newton method for simultaneous design and optimization
The paper deals with a design optimization problem where the constraint is a state equation: (P) min \(f(y,u)\) s.t. \(c(y,u)=0\) where \(y\) denotes the state and \(u\) the design variable. It is assumed that the state \(c(y,u)=0\) can be transformed into a fixed point equation \(y=G(y,u)\). Then (P) is transformed into an equality constrained optimization problem of the form: (PG) min \(f(y,u)\) s.t. \(y=G(y,u)\). The authors use the Lagrangian of (PG) to append the primal iteration with the dual and preconditioned design iterations. The coordination of the three iterative process is guaranteed by using an exact penalty function of double augmented Lagrangian type. Under certain assumptions global convergence of the optimization approach is proved. Finally, some numerical experiments done on a variant of the Bratu problem are presented.
scientific article; zbMATH DE number 5915216
scientific article