Practical Least pth Optimization of Networks

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Abstract
A new and practical approach to computer-aided design optimization is presented. Central to the process is the application of least pth approximation using extremely large values of p, typically 1000 to 1000000. It is shown how suitable and reasonably well- conditioned objective functions can be f ornndated, giving particular emphasis to more generaf approximation problems as, for example, in filter design. It is demonstrated how easily and efficiently ex- tremely near minimax results can be achieved on a dkicrete set of sample points. Highly efficient gratlent methods can be employed and, in network design problems, the use of the adjoint network approach for evaluating gradients results in greater savings in com- puter effort. A comparison between the Fletcher-Powell method and the more recent Fletcher method is made on the application of least pth approximation, using a range of valuesofpupto1000000 000000 on transmission-line transformer problems for which optimal mini- max solutions are known. This is followed by filter design examples sub ject to certain constraints.

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