Optmization of nonconvex nonconcave problem using iterative approach
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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
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/165411/image.png)
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.
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