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I am trying to implement the following optimization (from this paper) in Matlab using fmincon:

$\min_\omega\omega'\Sigma\omega$ subject to $\min_Ur_p \geq r_0$

where $\Sigma$ is a positive definite matrix and $\omega$ is a vector of weights that sum to 1. Also, we have $r_p=\alpha'\omega$ and $U$ is the circle centred at $\alpha$ with radius equal to $|\chi|\alpha$ for $\chi$ between 0 and 1.. The authors of the paper show that:

$\min_Ur_p=|\alpha||\omega|[cos(\phi)-\chi]$ where $\phi$ is the angle between the two vectors $\alpha$ and $\omega$.

Any ideas how to implement this using matlab?

edited Feb 3 at 13:23

asked Feb 3 at 0:10

Geraldine Bailey
13●3

Your constraint doesn't make sense as stated. Are you trying to say something like $$\min_{\chi\in[0,1]} |\alpha||\omega|[\cos\phi - \chi]=r_p$$ for some given $r_p$? Is $\Sigma$ positive semidefinite? Who are "the authors"? If this is a convex problem, you're probably much better off using cvx rather than fmincon. – John Gunnar Carlsson Feb 3 at 3:30

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The poster has also put this same question up on scicomp.stackexchange.com, where she's somewhat more likely to get a useful answer, provided that she can clarify the question. – Brian Borchers Feb 3 at 4:19

Hi there, I seem to have left out a minor detail in my initial post. I have corrected this now. – Geraldine Bailey Feb 3 at 12:48

meij · Answer 1 · 2013-02-03 00:41:20Z UTC

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Your in the wrong forums go to http://scicomp.stackexchange.com/.

answered Feb 3 at 0:41

meij
227●1●4

	@Teo B: If you would like to encourage this question then it could be more constructive to edit it so that it could be understood by those of us who do not have enough points to see its unformatted text. – meij Feb 3 at 1:27
	This is not an answer. I do know you cannot yet comment, but then do not (in particular if there is no urgency). – quid Feb 4 at 18:02
	@quid: The OP went to the on-topic forum that I suggested, where the question has now been answered and accepted. If your mad about this sequence of events, possibly because the original question was not researchy enough, then maybe you should just close or delete the question, or just start hanging out at the stackexchange suggested by Teo B? – meij Feb 4 at 18:11
	Could you please read what I wrote, before guessing around why I am mad. In detail: I am mad (to the extent I am mad about such things) that you gave an answer that did not answer the question in anyway. It did not answer it, not even partially, right? (This is completely independent of the question.) An issue with such answers that might not be apparent is that they tend not to get upvoted or accepted and then the community user will push this question up and up again to the frontpage. Okay, I now changed my downvote to an upvote. Also a way to solve that problem. – quid Feb 4 at 19:38

Robust optimization in matlab using fmincon

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