A globally most violated cutting plane method for complex minimax problems with application to digital filter design (Q1315252)

This paper is concerned with the generalized complex Chebyshev- approximation problem: \[ \text{Minimize}\qquad F(h):= \max_{1\leq j\leq m} \max_{\omega\in\Omega_ j}\left| D_ j(\omega)- \sum^ N_{n=1} h_ n \phi_{n,j}(\omega)\right|^ p, \] over all elements \(h:= (h_ 1,\dots,h_ N)^ T\) of a nonempty closed parameter set \(H\). The authors consider a direct approach for the solution of general convex semi-infinite programming problems. The algorithm is based on the use of the globally most violated constraint. Some interesting numerical examples are discussed.