An algorithm for computer aided design problems

A large class of engineering design problems including multivariable feedback systems, can be transcribed into the form P: min{f0(x)|gj(x)¿0 j = 1,.., q, j¿¿¿ max fj(x,¿)¿0, j = 1,..., m}, with each ¿j a bounded interval of the real line. In this paper we give several examples of such transcriptions, including that of an i.s.e., PID controller design for a single-input single-output system subject to a phase-margin constraint and a peak overshoot-settling time problem. We then present scaling procedures for the search vector in the Polak-Mayne [1] algorithm which solves P, as well as a new, self-scaling, algorithm for solving P. This new algorithm is related to the Pironneau-Polak [6] dual method of feasible directions. The use of scaling in such methods is most important since it leads to substantial savings in computing time.