11-hw116 - MATHEMATICS 116, FALL 2007 CONVEXITY AND...

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

View Full Document Right Arrow Icon
MATHEMATICS 116, FALL 2007 CONVEXITY AND OPTIMIZATION WITH APPLICATIONS Assignment #11 Last modified: December 12, 2007 Due Tuesday, December 18 at class. If you are leaving town early, deliver it early to Nike. Work the last two problems before Thursday, since they are useful background for the applications that will be done in class. 1. Luenberger, Exercise 5.14.16. This is a crucial part of the Lagrange multi- plier rule in section 7.7. 2. State and prove all the theorems on pages 187-188 of Luenberger, simplified to the case n = 2. 3. Luenberger, problem 7.14.12. In lecture the problem was solved for arbi- trary boundary conditions x ( - 1) and x (1). In polar coordinates the solu- tion is simple when x ( - 1) = 0 and x (1) = 0, and you need do only that case. You may have to hunt up your old calculus text to get formulas for area and arc length in polar coordinates. It is very easy, once you have the differential equation, to show that r ( θ ) = 1 is a solution, and I think that is what Luenberger had in mind. However,
Background image of page 1

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

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

Page1 / 2

11-hw116 - MATHEMATICS 116, FALL 2007 CONVEXITY AND...

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