In Stephen Boyd’s Convex Optimization book, an example of a quasiconcave problem is provided in Example 3.34 and is known as the internal rate of return. Does anyone know how to formulate the convex set mentioned using CVX?
I understand that this problem is quasiconcave and not directly handled by CVX. However, I am aware of techniques to handle quasiconvex/quasiconcave problems (i.e. Algorithm 4.1 in the aforementioned book). My question is focused on representing the convex set mentioned in the problem.
The problem says that \text{IRR}(x) \ge R \Longleftrightarrow \text{PV}(x,r)>0 \; \text{for} \; 0\le r<R represents a convex set. Is there a way to represent this set in CVX?
Would it make sense to use the bisection method where f_0(x) := -\text{IRR}(x), t:=r to follow the approach in equation (4.26) of the aforementioned book? Therefore, starting with l=0,u=R, we could use the bisection algorithm (keeping the l=0 to ensure we find the minimum r) to find the optimal x at the minimum r?