On Fri, Mar 24, 2017 at 8:43 PM, saiket talukdar <

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> I am trying to optimize a root function of the form MIN root(x'CX)

> ST u'x=u

> E'x=1

> Where both u and E are column vectors and c is a square matrix .can anyone

> say how to model this in QP?

>

>

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What do you mean by 'root'? In general, the roots of a second degree

polynomial over multiple variables doesn't form a discrete set, so you

will have troubles with this optimization. Analyze the case p(x,y) =

x^2 - y^2 (C = [1 0; 0 -1]), the roots are all pairs |y| = |x|, i.e.

(x,x), (x,-x), (-x,x) for any complex x. So how would you choose the

min of these? maybe MIN abs(root(x'Cx))?

Also if C is positive definite quadratic form, you can diagonalize it

and solve the diagonal problem sum(L_i * y_i^2), with L_i the

eigenvalues of C., This means you will work on y = S x, where S is the

orthogonal matrix that diagonalizes C (use svd), but in this case you

are bound to find complex roots.

Finally, I do to think root(x'*C*x) can be reduced to a quadratic

form, hence QP is not the right tool. Try sqp, but again, be careful

the solutions might be infinite and you need to disambiguate with your

cost function to make one of all the possible infinite roots the

minimum.

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