We introduce a technique for designing homogeneous magnets using linear pro
gramming, We first show that minimum-power homogeneous magnet design can be
cast as a linear programming problem. We also show that the method is appl
icable to minimum conductor mass superconducting magnet design. The method
has several advantages over existing techniques including: it allows comple
te flexibility in arbitrary geometric constraints on both the coil location
s and the shape of the homogeneous volume; it guarantees a globally optimal
solution; and it offers rapid computation speed (about 30 s), Three resist
ive magnet design examples and one shielded superconducting magnet design a
re presented to illustrate the flexibility of the method.