Optmization of nonconvex nonconcave problem using iterative approach

 I am trying to implement a profit optimization function in a cloud computing environment. Objective function is claimed to neither convex and nor concave. The function along with constraints is given as under

The authors say that objective function becomes convex if we solve it iteratively that is first fixing P_jk and optimize φ_jk and vice versa till solution converge. I am not sure whether this is a right argument. Secondly, I have implemented the problem using Matlab fmincon, after running optimization, the value of phi (optimized) is set to all 1s, meaning 100% resource utilization which is not practically true. For example, if we have a cloud with 48 servers and 30 processing tasks to be executed, they would be assigned to any of the 30 servers whose phi may be between 0 to 1 but for rest of the servers, phi should not be 1. If you can kindly comments on this issue also? Is my understanding correct? Thirdly, if fmincon is a right tool to use in this case? I shall appreciate any help.