A new mathematical programming time-sharing system using a precompiler and numerical derivatives

One approach for allowing a problem-oriented user to easily state and solve a given problem on a time-sharing system is by using a precompiler. The precompiler recognizes statements in a simple problem-oriented language, generating corresponding computer instructions and subprograms. These are used to define the problem and select the solution algorithms from a software library. To illustrate this approach, a simple Fortran precompiler has been implemented for the Univac which accepts mathematical programming commands (e.g. MINIMIZE:, SUBJECT TO:, etc.) and allows certain standard algorithms to be invoked. In order for this mathematical programming system to be genuinely easy to use, the required gradients and Hessians are approximated by accurate Richardson extrapolated difference schemes.