User-oriented computer programs in FORTRAN IV for discrete least pth approximation with a single specified function, and more generalized discrete least pth approximation with various specifications, which may also be used for nonlinear programming, are presented. Values of p up to 10^6 can be used successfully in conjunction with efficient gradient minimization algorithms such as the Fletcher-Powell method and a recent method due to Fletcher. It has already been demonstrated how efficiently extremely near minimax results can be achieved on a discrete set of sample points using this approach and the programs written verify this. The programs may be applied to a wide variety of design problems with a wide range of specifications. They are suitable for electrical network and system design and such problems as filter design.