Optimization when beq is zeros
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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.
2 Comments
Andrew Newell
on 12 Apr 2011
How do you know that all zeros is a trivial solution? Are all the components of c nonnegative?
Answers (1)
Laura Proctor
on 12 Apr 2011
There's also a webinar called Tips & Tricks - Getting Started Using Optimization with MATLAB that could be pretty helpful.
2 Comments
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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