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Limitations of Minimize? Time to buy a new PC for Mathematica?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg113068] Limitations of Minimize? Time to buy a new PC for Mathematica?
  • From: Adrian Boyko <adrianboyko at gmail.com>
  • Date: Tue, 12 Oct 2010 04:29:21 -0400 (EDT)

  Hi,

I'm new to the list and a casual user of Mathematica at home.  So, I 
hope you'll forgive what might be a basic or silly question.

I'm trying to perform linear least squares with constraints (all x's > 
0) and somebody suggested I might be able to do this with Minimize.  
When I run the following, Mathematica works on it for a very long time 
(not sure how long, since I didn't sit at the computer waiting for it to 
finish) and then finally returns "No more memory available."  Two questions:

Q1: Is this problem just too much to ask of Mathematica or can it be 
solved if I upgrade my low-end PC to something new with 8 or 12 GB of 
RAM?  I don't want to buy a new machine just to discover that no amount 
of RAM will help.

Q2: Is there a more memory-efficient way to solve this sort of problem 
in Mathematica?

Thanks, in advance, for any help or comments!


Minimize[
    {
       + (660-x24)^2 + (341-x0-x12-x15-x17-x32)^2 + (528-x0-x15-x24-x33)^2
       + (266-x24)^2 + (263-x0-x9-x12)^2 + (181-x17)^2 + (353-x14)^2
       + (120-x0-x12-x15-x33)^2 + (149-x0-x12-x14-x15-x33)^2
       + (215-x0-x12-x17-x32)^2 + (566-x20)^2 + (777-x0)^2 + (94-x24)^2
       + (56-x15)^2 + (53-x12)^2 + (351-x24)^2
       + (426-x0-x12-x15-x17-x24-x33)^2 + (477-x24)^2 + (357-x12)^2
       + (548-x0-x12-x32)^2 + (210-x17-x24)^2 + (167-x9)^2
       + (173-x0-x12-x20)^2 + (77-x17-x24)^2 + (173-x20-x38)^2
       + (218-x0-x12-x14-x15-x20-x38)^2 + (217-x0)^2 + (482-x0-x12)^2
       + (252-x12)^2 + (312-x24)^2 + (212-x17)^2 + (606-x17)^2
       + (337-x9)^2 + (831-x0)^2 + (212-x0-x9-x12-x15-x32-x33)^2,
       {
          x0 > 0 && x9 > 0 && x12 > 0 && x14 > 0 && x15 > 0 && x17 > 0
&& x20 > 0 && x24 > 0 && x32 > 0 && x33 > 0 && x38 > 0
       }
    },
    {x0, x9, x12, x14, x15, x17, x20, x24, x32, x33, x38}
]



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