A Language for Nonlinear Programming Problems.
Abstract
The paper describes an algebraic-like language for nonlinear programming problems and the rationale for the computer implementation of the language. The language provides for the computation of the function values, gradients, and second partial derivatives of the functions of a programming problem at specified points in space. Each function is translated into an explicit 'factorable' form whereby it is expressed as the transformation of the sum of a set of products and each factor of each product may in turn be a transformation of the sum of a set of products. This hierarchical representation terminates when a factor of a product is a function of a single variable. For a given point in space the value, gradient, and second partials of each function are computed in turn so that each computational step makes use of the results from the preceding step. The matrix of second partials for a function at a point is represented as a set of vector outer products, the vectors having resulted from the gradient computation, plus a diagnonal matrix. The organization and experience with the operational computer program which implements the language and ties it to SUMT are described. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1970
- Accession Number
- AD0715372
Entities
People
- Robert E. Pugh