Minimization with constraint involving logs in Julia

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Albert John Crosby

2024年03月13日 21:46 編集済み

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I want to solve \(\frac{1}{N} \sum_{i=1}^N x_i^2\) subject to \(\frac{1}{N} \sum_{i=1}^N \log x_i \geq 0\). 

In the above, N is the size of the vector x whose \(i^{th}\) element is \(x_i\). I think the solution should be \(x_j = 1\), for all \(j=1,\ldots, N\). How do I code this in Julia? I appreciate that I could replace the constraint involving a sum by a product but in the true application I have in mind (which involves logs) this may not be possible. Basically I want to minimize a function which is convex and straightforward but with a constraint involving logs. I tried the following but it doesn't work. In the below, ncol is the size of n (which is denoted x above)

model = Model(Gurobi.Optimizer)
@variable(model, 1000.0 >= n[1:ncol] >= 0.001)
@objective(model, Min, sum(n[i]^2 for i in eachindex(n)) / ncol)
@expression(model, expr, sum(log(n[i]) for i in 1:ncol))
@NLconstraint(model, expr >= 0.0)
optimize!(model)

 

  Can anyone tell me how I could incorporate a constraint on the log of x? The code is Julia.

Thank you. 

 

関連

• Nonlinear
• Julia

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  Simranjit Kaur

  • Gurobi Staff

  2026年11月13日 01:28

  This post is more than two years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum, or try Gurobot, our chatbot interface offering instant, expert-level support.
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  David Torres Sanchez

  • Gurobi Staff

  2024年03月18日 11:56 編集済み

  See a similar post in the Julia discourse. In your case, you can use the GRBaddgenconstrLog which is documented here: GRBaddgenconstrLog - C API.

  Cheers, 
  David

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