Linear best approximation using a class of polyhedral norms

A class of polyhedral norms is introduced, which contains thel1 andl∞ norms as special cases. Of primary interest is the solution of linear best approximation problems using these norms. Best approximations are characterized, and an algorithm is developed. This is a methods of descent type which may be interpreted as a generalization of existing well-known methods for solving thel1 andl∞ problems. Numerical results are given to illustrate the performance of two variants of the algorithm on some problems.