THE LAGRANGE MULTIPLIER, A HEURISTIC PRESENTATION
CENTER FOR NAVAL ANALYSES ALEXANDRIA VA OPERATIONS EVALUATION GROUP
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Many problems in operations research require the maximization or minimization of a suitable payoff function subject to various constraints. Lagrange multipliers are classically used for this type of problem, however, the treatment given this technique by most texts requires that the payoff and constraint functions be at least differentiable at the extremizing point. This paper shows that the Lagrange multiplier concept can be independent of differentiability or even continuity of the functions involved. It also gives the reader a geometric insight into the workings of the multiplier. Simplifications possible, if the functions involved are homogeneous, are displayed. The treatment is heuristic rather than formally rigorous.
- Operations Research