HW6solutions

# HW6solutions - MS&amp;amp;amp;E 211 Linear &amp;amp;amp;...

This preview shows pages 1–3. Sign up to view the full content.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MS&amp;E 211 Linear &amp; Nonlinear Optimization Fall 2011 Prof Yinyu Ye Homework Assignment 6 Solutions 1. Log-Barrier Method: [25points] (a) [10points] Solve using the log-barrier method: gGGG: + 3 + : + = 1 , 0 Equalities cant be made into a barrier, and so we substitute: = 1 Thus the problem reduced to one variable: gGGG: 1 + : 0 The barrier function becomes: 1 + lo () Differentiating yields: 1 2 . Setting equal to zero and solving gives: 2 = 0 . Or = , which approaches 0 or Zero is the minimum, so using our substitution equation to get the other value, (0,1) is the optimal solution. (b) [10points] Solve using the log-barrier method: gGGG: 1 2 + 1 2 2 : + 4 The barrier function becomes: + 2 lo ( + 4) Differentiating and setting to zero yields: 1 = 0 2 = 0 Thus, in some optimality: = + 1 Substituting: 1 = 0 Simplifying: 2 5 + 3 = 0 Solving: g G = G Which converges to 1 and Using our substitution equation to get g , our two candidates are (1,2) and ( , ) Clearly one is the global minimum, and the other our answer. ( , ) (c) [5points] Explain why we can or cannot guarantee convergence to the optimal solution in...
View Full Document

## This note was uploaded on 01/16/2012 for the course MS&E 211 at Stanford.

### Page1 / 5

HW6solutions - MS&amp;amp;amp;E 211 Linear &amp;amp;amp;...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online