Nonlinear programming without computation

Abstract

Using the Kuhn-Tucker conditions from mathematical programming theory, a canonical nonlinear programming circuit for simulating general nonlinear programming problems has been developed. This circuit is canonical in the sense that its topology remains unchanged and that it requires only a minimum number of 2-terminal nonlinear circuit elements. Rather than solving the problem by iteration using a digital computer, we obtain the answer by setting up the associated nonlinear programming circuit and measuring the node voltages. In other words, the nonlinear programming circuit is simply a special purpose analog computer containing a repertoire of nonlinear function building blocks. To demonstrate the feasibility and advantage of this approach, several circuits have been built and measured. In all cases, the answers are obtained almost instantaneously in real time and are accurate to within 3 percent of the exact answers.