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Hello,

I do not yet have the optimization toolbox, but would like to ask if it can solve the following problem.

minimize c'*x

such that Aeq*x = beq, where beq = zeros and zeros < x

and zeros means a column vector of appropriate size in all cases. Please note that zeros < x, not zeros <= x. Of course, I realize that a trivial solution exists (x = zeros), but I seek a non-trivial solution.

In case anybody is wondering, this is a solution of a matrix null space problem with a constraint that all elements of the null space vector > 0.

Thanks.

Laura Proctor
on 12 Apr 2011

Teja Muppirala
on 13 Apr 2011

Any nontrivial solution could only be a linear combination of the columns obtained when you evaluate:

M = null(Aeq) * null(c'*null(Aeq))

I guess you could rephrase your question as:

Does there exist a z such that

M*z > 0

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