Feature Article—Survey of Nonlinear Programming Applications

Abstract

Several factors imply an increase in the use of nonlinear optimization models. We face serious problems of declining productivity and increasingly scarce, expensive raw materials. Computers are becoming cheaper and faster, and more efficient nonlinear programming (NLP) algorithms are being developed. This paper attempts to illustrate the potential of NLP by describing the application of nonlinear programming models to three classes of problems: petrochemical industry applications, nonlinear networks, and economic planning. Problems in the petrochemical industry ranging from product blending, refinery unit optimization, and unit design to multiplant production, and distribution planning are discussed. The nonlinear networks topic includes electric power dispatch, hydroelectric reservoir management, and problems involving traffic flow in urban transportation networks. In economic planning, we describe NLP applications involving large dynamic econometric models, a variety of static equilibrium models, and submodels of larger planning systems. In each area we consider the problem and its nonlinear model, the various algorithms and software systems which have been applied, and (where available) the benefits derived. Some obstacles are identified which currently inhibit the effective use of nonlinear optimization models, and research aimed at overcoming these obstacles is suggested. A comprehensive bibliography is included.