This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: When y=1, f(x, 1) = which has local minimum at (+√3/2). When y=1, f(x, 1) = for all x. 2/3 EE5239 HW1 So the global minima are f(+√3/2,1) = . 1.1.3 (a) . for (b) , so (0, 0) is a stationary point. i. Consider the line y=0, f(0, z) = f(0, 0) = 0 for , (0,0) is a local minimum along line y=0. ii. Consider the line z =0, f(y, 0) = f(0, 0) = 0 for , (0,0) is a local minimum along line z=0. iii. Now consider the general case: along line , . + We have = 2 > 0, so (0,0) is a local minimum along line , Then we can say that (0,0) is a local minimum of f along every line that pass through (0,0). If p < m <q, then , so (0,0) is not a local minimum of f. 1.1.4 Let 2, then x=1. for all x > 0, which means that is a convex function for . 3/3 EE5239 HW1 Then the global minimum is reached at , x=1. f(x) f(1) = 0 for all x > 0 . 4/3...
View
Full
Document
This note was uploaded on 04/30/2011 for the course MECHANICAL MSC taught by Professor Dr.rahula during the Spring '10 term at University of Moratuwa.
 Spring '10
 DR.RAHULA

Click to edit the document details