An Algorithm for the Chebyshev Problem---With an Application to Concave Programming

The Chebyshev problem is to determine a point xα which solves maxα min i = 1,..., N{gix}. By exploiting generalized inverses an algorithm is developed for determining xα. It is also shown that in a certain sense the Chebyshev problem is equivalent to the concave programming problem. Moreover, for the programming problem generated by the Chebyshev problem, the Kuhn-Tucker conditions are proven to be sufficient even though the feasible region may not be convex.