A nonlinearl_1optimization algorithm for design, modeling, and diagnosis of networks

This paper presents a fast and highly efficient algorithm for nonlinear
l_1
optimization and its applications to circuits employing the properties of the
l_1
norm. The algorithm, based on the work of Hald and Madsen, is similar to a minimax algorithm originated by the same authors. It is a combination of a first-order method that approximates the solution by successive linear programming and a quasi-Newton method using approximate second-order information to solve a system of nonlinear equations resulting from the first-order necessary conditions for an optimum. The new
l_1
algorithm is particularly useful in fault location methods using the
l_1
norm. A new technique for isolating the most likely faulty elements, based on an exact penalty function, is presented. Another important application of the algorithm is the design of contiguous-band multiplexers consisting of multicavity filters distributed along a waveguide manifold which is illustrated by a 12-channel multiplexer design. We also present a formulation using the
l_1
norm for model parameter identification problems in the presence of large isolated errors in measurements and illustrate it with a sixth-order filter.