Revision as of 09:47, 27 January 2015

QE2013_AC-3_ECE580-4

(i)
Solution:
$$ x(3) = x(2) + 2u(2) = x(1) + 2u(1) + 2u(2) = x(0) + 2u(0) + 2u(1) + 2u(2) $$

$\because x(0) = 3, x(3) = 9$

$\therefore \ Constraint: 2u(0) + 2u(1) + 2u(2) = 6$

Let $$ f(u) = u^2(0) + u^2(1) + u^2(2), h(u) = 2u(0) + 2u(1) + 2u(2) - 6 $$

Let u* be a local minimizer. Lagrange theorem says there exists a λ such that:

$\nabla f(u*) + \lambda \nabla h(u*) = 0 \\ h(u*) = 0$ Back to QE2013 AC-3 ECE580

@@ Line 18: / Line 18: @@
 <math>\therefore \ Constraint: 2u(0) + 2u(1) + 2u(2) = 6 </math>
+Let <math>f(u) = u^2(0) + u^2(1) + u^2(2), h(u) = 2u(0) + 2u(1) + 2u(2) - 6 </math>
+Let u* be a local minimizer.  Lagrange theorem says there exists a λ such that:
+<math>\nabla f(u*) + \lambda \nabla h(u*) = 0 \\
+      h(u*) = 0 </math>
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