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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

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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.

m7913d
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sukhalid
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  • There seem to be two different `f1`'s in the objective. – Erwin Kalvelagen Jun 22 '17 at 05:06
  • I am sorry there were two typos, now I have corrected them. – sukhalid Jun 22 '17 at 05:29
  • Not sure if this iterative scheme is guaranteed to converge to the optimal solution. For non-convex problems always try different starting points to see if there are multiple local optima. Otherwise use a global solver such as Baron, Couenne or Antigone. – Erwin Kalvelagen Jun 22 '17 at 18:27

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