Nov 30 fix up

Nov 30 fix up - guarantee that j x is positive for at least...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Fix Up Question: The data in the optimization problem that appears below are positive numbers 1 a through m a and positive numbers 1 b through m b . What is its optimal solution? Why? Minimize = m 1 j 2 j j ) x ( a , subject to λ : 100 x b m 1 j j j = = . Answer: The objective is convex and differentiable, and the constraints are linear, which assures us that Hypothesis #1 is satisfied. Thus, the KKT conditions are satisfied at x if and only if x is an optimal solution. Taking partial derivatives and using the ross-over table shows us that the KKT conditions are: j x : j j j x a 2 b = λ for j = 1, 2, …, m . The constraint of the NLP and the fact that 1 b through m b are positive
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: guarantee that j x is positive for at least one j, say, for j = 2. The equation 2 2 2 x a 2 b = demonstrates that is positive and that 2 2 2 a 2 b x = . And the equation that is complementary to j x guarantees (1) j j j a 2 b x = for j = 1, 2, , m . Multiply equation (1) by j b , sum over j, and then substitute into the constraint of the nonlinear program to see that ] a / ) b [( 200 k m 1 k 2 k = = , and then use (1) to see that the optimal solution to this nonlinear program is ] a / ) b [( a / b 100 x k m 1 k 2 k j j j = = for j = 1, 2, , m ....
View Full Document

Page1 / 2

Nov 30 fix up - guarantee that j x is positive for at least...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online