asst4 - CO 355 Mathematical Optimization (Fall 2010)...

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

View Full Document Right Arrow Icon
CO 355 Mathematical Optimization (Fall 2010) Assignment 4 Due: Thursday, November 11th, in class. Policy. No collaboration is allowed. You may use the course notes / textbook and the lecture slides, but please be very specific when using citing results found there. (Don’t just say “from some claim in class we know. ...”.) Every other resource that you might stumble upon must be properly referenced. You are welcome to seek help from the current instructor and TAs for CO 355. Question 1: (10 points) [Exercise 3.2.3] Let S R n be a convex set and f : S R be a convex function. For any points x 1 ,...,x m S and scalars λ 1 ,...,λ m 0 with m i =1 λ i = 1, prove that f m X i =1 λ i x i ! m X i =1 λ i f ( x i ) . Question 2: (15 points) [Exercise 3.2.7] (a): Let R ++ = { x R : x > 0 } . Let g : R ++ R be defined by g ( x ) = - log( x ). (This is the natural logarithm.) Prove that g is convex. (b):
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.

This note was uploaded on 06/16/2011 for the course CO 355 taught by Professor Harvey during the Winter '10 term at Waterloo.

Page1 / 2

asst4 - CO 355 Mathematical Optimization (Fall 2010)...

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