
Linear Algebra Linear Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
December 16th, 2007, 06:03 AM  #1 
Newbie Joined: Dec 2007 Posts: 3 Thanks: 0  Optimization of a Matrix with one constraint.
Hello! I have a minor problem, that wont get solved... Its been posted in an old competition at our university, but I didnt manage to solve it in time. Maybe someone in here could help me? Where D is a symmetric n x n matrix, and x is an unknown n x 1 vector. I can only figure out how to test for a maximum later on, but is there something im missing with the charataristic roots? Regards 
December 16th, 2007, 04:56 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,560 Thanks: 605 
I must confess I'm a little rusty here. However by taking first derivatives with respect to each of the xi, you will end with a matrix equation with (x1,....,xn) any eigenvector, as a solution. Normalize the eigenvectors to unit length and see which one gives you the maximum.

December 16th, 2007, 10:37 PM  #3 
Newbie Joined: Dec 2007 Posts: 3 Thanks: 0  
December 17th, 2007, 01:11 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,560 Thanks: 605 
If you look at the line which says "D is symmetric" and you make the equations into one big vector, you will have Dx=Lx (L=lambda), which means the solution is an eigenvector and L is an eigenvalue. In general there will be n solutions.


Tags 
constraint, matrix, optimization 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
constraint problem  helloprajna  Economics  0  February 17th, 2013 11:04 PM 
Help with budget constraint and utility maximisation  palarce  Economics  0  May 7th, 2012 05:59 AM 
Matrix norm optimization problem  onako  Linear Algebra  0  February 1st, 2012 12:59 AM 
Derivative with a range constraint  Gekko  Calculus  3  June 12th, 2010 09:16 AM 
Optimization Problem with Constraint  Justin Lo  Applied Math  0  December 8th, 2009 02:40 AM 