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

The Chebyshev problem is to determine a point x α which solves max α min i = 1,…, N{g i (x)}. By exploiting generalized inverses an algorithm is developed for determining x α . 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.

• 저널Management Science · 14(1) · 58–78
• 토픽Matrix Theory and Algorithms · Computational Theory and Mathematics
• DOI10.1287/mnsc.14.1.58
• 저자Willard I. Zangwill