LFD Book Forum Quadratic programming
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#1
08-23-2012, 06:28 AM
 invis Senior Member Join Date: Jul 2012 Posts: 50

I never used QP in my practice. And I using Octave for solve HWs.
So there is built-in function for quadratic programming in Octave - qp. (example)

But I still dont know what parameters I should use to solve:

s.t.

Looks like H is (.* is element by element product)
But what is the other parameters
#2
08-23-2012, 10:09 AM
 invis Senior Member Join Date: Jul 2012 Posts: 50

And where is ?
#3
08-23-2012, 11:23 AM
 invis Senior Member Join Date: Jul 2012 Posts: 50

I am absolutly confused

Should I use QP to solve this inequality:

s.t.

OR to solve inequality in picture in previous message ?
#4
08-23-2012, 05:22 PM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,477

Quote:
 Originally Posted by invis I am absolutly confused Should I use QP to solve this inequality: s.t. OR to solve inequality in picture in previous message ?
The version in the picture. It's the dual problem (equivalent) to the version that is in the quote.
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#5
08-24-2012, 04:40 AM
 invis Senior Member Join Date: Jul 2012 Posts: 50

Why sometimes it is impossible to find the solution and what to do with that ?
On 200 iterations with random line and random dots (#10) 81 times QP didnt find the solution (I plot the line and dots for this situations and all looks pretty clear).
This is the parameters for QP I use:

H = (Y*Y') .* (X*X');
A = Y';
q=-1*ones(n,1);
b=0;
lb=zeros(n,1); (lower bound)
ub=[]; (upper bound)

min 0.5 x'*H*x + x'*q
subject to

A*x = b
lb <= x <= ub

where x is our
#6
08-24-2012, 05:30 AM
 htlin NTU Join Date: Aug 2009 Location: Taipei, Taiwan Posts: 601

Quote:
 Originally Posted by invis Why sometimes it is impossible to find the solution and what to do with that ? On 200 iterations with random line and random dots (#10) 81 times QP didnt find the solution (I plot the line and dots for this situations and all looks pretty clear). This is the parameters for QP I use: H = (Y*Y') .* (X*X'); A = Y'; q=-1*ones(n,1); b=0; lb=zeros(n,1); (lower bound) ub=[]; (upper bound) min 0.5 x'*H*x + x'*q subject to A*x = b lb <= x <= ub where x is our
Sometimes the numerical condition of the optimization problem makes it hard for the solver to locate a good solution. One possibility is to set ub (upper bound) to a really large value. Hope this helps.
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#7
08-24-2012, 05:42 AM
 invis Senior Member Join Date: Jul 2012 Posts: 50

I change ub to:
ub=10^22*ones(n,1);

For 400 iterations 154 without solution How to deal with it in context of homework ?
"How often is
better than in approximating ?"
#8
08-24-2012, 06:03 AM
 jakvas Member Join Date: Jul 2012 Posts: 17

@invis

for the 100 points problem 400 iterations may be too little (i used 2000 iterations in my matlab code and in ~2% of the cases even that limit was exceeded but that still gives a decent accuracy you could use even more but don't go too far or you will never get results) also for the upper bound I used 10^5 and 10^10 without any significant change in results, 10^22 seems a bit much considering you are probably using single precision numbers
#9
08-24-2012, 06:10 AM
 invis Senior Member Join Date: Jul 2012 Posts: 50

400 iterations I use only to show that ~40% of problems QP cant solve even with 10 dots. So how can I compare results with PLA ?

Jakvas you are using matlab, so maybe you can tell me am I miss something in parameters for QP ? Why almost half of problems without solution ?
#10
08-24-2012, 06:17 AM
 jakvas Member Join Date: Jul 2012 Posts: 17

try a smaller upper bound and maybe plot some of the results you do get to see if there is no serious error somewhere.

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