EIN%206336%281%29

# EIN%206336%281%29 - EIN6336...

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Click to edit Master subtitle style  2/16/11 EIN 6336  Background Material

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2/16/11 We will first consider Lagrangian optimization Consider the following optimization problem Minimize f(x, y) =  x/2 + 2y Subject to:  xy = 4 This is an easy problem to solve: Substitute y = 4/x in the objective: Minimize x/2 + 8/x Take the derivative and set it equal to zero: ½ - 8/x2 = 0, or x  = 4.  y = 4/x = 1. Appendix A
2/16/11 How do we know that x = 4 provides a global  minimum? We considered the unconstrained minimization of  f(x) = x/2 + 8/x A zero derivative would imply a globally optimal  solution if this function is  convex   A differentiable function of one variable is convex  if and only if the second derivative is nonnegative Appendix A

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2/16/11 We wish to discuss Lagrangian optimization for  problems of the following form: Minimize  f(x, y)  Subject to: g(x, y) = 0 We create a Lagrangian function
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## This note was uploaded on 02/15/2011 for the course EIN 6336 taught by Professor Staff during the Spring '08 term at University of Florida.

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EIN%206336%281%29 - EIN6336...

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