How to implement following function $\sum\limits_i {\sum\limits_k {{y_i}\log (1 + \frac{{x_i^k}}{{{y_i}}})} } $

2

Using mcg’s “trick” from x\log(1+1/x) using CVX , each term of the double summation can be expressed as -rel_entr(y(i)+x(i)^k,y(i)) , which is DCP-compliant and convex. So the entire double summation is a sum of DCP-compliant convex terms, and hence is DCP-compliant convex.

Edit: each term should be -rel_entr(y(i),y(i)+x(i)^k)

1 Like