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I am trying to derive ELM going through the basics , please help me out here :

$$f = x^Tx$$ $$g = Ax-b $$

The constraint is $Ax-b = 0$

I calculated $J' = f'+\lambda^T g'$ which is $2x+(\lambda^T A)^T = 0 $ and $Ax-b=0$ . I dont know what to do next please help me out .

abkds
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  • Please tell us what ELM means. It looks like you are asking for help solving a Lagrange multiplier problem, right? – whuber Feb 25 '14 at 21:46
  • Extreme Learning Machine – abkds Feb 25 '14 at 21:47
  • That term is irrelevant , its just an optimization problem – abkds Feb 25 '14 at 21:47
  • answer should $x = pseudoinverse(A)b$ but I am not able to derive it – abkds Feb 25 '14 at 21:48
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    This is solved in many, many places on this site: the key is to recognize that your are trying to solve the least squares equations and the solutions are given by [normal equations](http://stats.stackexchange.com/search?q=normal+equations). Follow the links in this search for your choice of demonstrations. I'll close this thread and provide a link to the first hit in the search (ordered by relevance). – whuber Feb 25 '14 at 21:55
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    TrafalgarLaw - it may help to check out the link that whuber suggests, and if it's still not clear, to ask a much more specific question. – Glen_b Feb 25 '14 at 22:01

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