Linear fractional objective

Nonconvex
1

Hi,

I have a problem of the form
min \sum_i x_i/ y_i
st.
A * [x;y] \ge 0

where x,y are 1-d positive variables.

This problem is convex but i dont know how to write a cvx problem for it. Any ideas?

ps
for a single element in the sum you define
f(t) =min_{x,y} x-ty
and if you find t^, such that
f(t^) =0
you can get the optimal solution.
and value of t^* can be found with a binary search…

2

Actually, no, it is not convex.

3

You probably did not notice I wrote x_i , y_i are positive, and as far as i can tell it means that x/y is convex and hence \sum x_i/y_i, am i missing something?

4

I am afraid that is simply incorrect. Compute the Hessian for f(x,y)=x/y and check its eigenvalues at, say, (x,y)=(1,1).

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