Domain rescaling techniques for the solution of affinely parametrized nondifferentiable optimal design problems

The authors show that the affine parametrizations used in the design of feedback compensators and open-loop optimal controls can lead to severely ill-conditioned optimization problems. The effect of this ill-conditioning is to cause many optimization algorithms to converge very slowly. They describe a domain rescaling technique which considerably mitigates this ill-conditioning. The technique is applied to both differentiable and minimax problems. A numerical example of a minimax problem involving two scaling matrices is given.<>