Abstract
This survey paper reports on the application of goal programming techniques toward the solutions of nonlinear field problems. The proposed approach involves approximating the solution by a set of trial functions containing unknown coefficients. The technique then minimizes in a weighted residual sense the absolute deviations of the system equations and/or the performance function residuals by nonlinear goal programming. Since the approximate solutions will in general not be able to satisfy all conditions, such as the boundary and initial conditions and at the same time minimize the residual errors, our approach involves reformulating the field problem as a preemptive goal programming model via the use of hard and soft constrains (or stiff and weak springs) in linear programming (or mechanics). Examples from fluid dynamics and control theory will be employed to illustrate the methodolgy. In conclusion, the advantages, limitations and other related issues on the goal programming model in solving nonlinear problems will be discussed.Key wordsGoal programmingMethod of Weighted ResidualsFluid DynamicsOptimal Control
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