A language for nonlinear programming problems

An algebraic-like language for nonlinear programming problems is described. The rationale for the computation of the function values, gradients, and sēcond partial derivatives of the functions from their algebraic representation is developed. Each function is translated into an explicit “factorable” form or hierarchical representation which is used interpretively to compute the function value, gradient, and second partials of the function at each point for which such values are required. Computational efficiency is achieved by computing the matrix of second partials as the sum of a set of vector outer products, the vectors having resulted from the gradient computation, plus a diagonal matrix. An experimental computer program which implements the language and ties it to SUMT is described. In the experience with this program the computer times required have ranged from 4 to 30 times those times required by computer solutions to the same problems by using analyst-prepared programs to compute the function values, gradients, and second partial derivatives. A program based on a compiler approach to implementing the language, rather than the interpretative approach of the experimental program, will probably result in computer times between one and two times those required by using analyst-prepared programs.