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This article discusses the Technique of Lagrange Multipliers, a powerful method for finding the local maxima and minima of functions subject to equality constraints. An example illustrates how to apply this technique to maximize P(det), the probability of detection, while adhering to a specified maximum acceptable probability of false alarm (PFA). Through a step-by-step analysis, we demonstrate how to set up the Lagrangian, derive the necessary equations, and ultimately find the optimal solution. This approach is essential for effective decision-making in various applied fields.
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_______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ Next: “Review” Technique of Lagrange Multipliers; include example; Then apply Method of Lagrange Multipliers to Maximize P(det), subject to a constraint of: a maximum acceptable PFA.
