Lecture06-2004 - Lecture VI An Introduction into...

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Lecture VI An Introduction into Multivariate Unconstrained and Constrained Optimality I. The development of the first and second order necessary conditions for the multivariate function. Like the univariate case, the development of the mulutivariate optimum is based on the Taylor series expansion. The multivariate form of the Taylor series expansion is typically restricted to the first two moments by convience, as f x f x f x dx dx f x dx xx x () ( ) ' ** * =+ + 1 2 2 . Again subracting f(x * ) from each side we are left with f x f x f x dx dx f x dx x () ( ) ' −= + 1 2 2 0 for a maximum at x * . II. Development of the Constrained Optimum The first stage in our discussion will be a fairly general description of the problem at hand. We are now interested in developing the optimality conditions for the problem max ( ) x fx st G x b = where f(x) is a scalar valued function mapping Gx Gx Gx dx x ( ) () ≈+ ∇= x n n mm m n Gx x x x x x x x x x
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This note was uploaded on 11/08/2011 for the course AEB 6533 taught by Professor Moss during the Fall '08 term at University of Florida.

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Lecture06-2004 - Lecture VI An Introduction into...

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