Can I use Gurobi to solve this convex optimization problem?

Awaiting user input

wenxin zhou

• December 26, 2021 12:34

I need to solve the following problem:

where v_t is fixed, V(u) is a concave function, V(u)=inf{f(v,u):v∈Ω}. Once u is known, the value and gradient of V(u) can be easily obtained, but we don't know the explicit expression of the objective function. The constraints of u, namely the big U, are box constraints (e.g., l<=u<=h). My problem is, can I just use Gurobi to solve this problem, or I have to use iterative algorithm to obtain the result?

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• Official comment

  

  Simranjit Kaur

  Gurobi Staff

  • December 06, 2024 00:21

  This post is more than three 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 why not try our AI Gurobot?.
• 

  Mario Ruthmair

  Gurobi Staff

  • December 28, 2021 07:32

  Hi Wenxin,

  To use Gurobi, you need to explicitly write a model with an objective function, so in your case you need to know f(v,u).
  You said that once u is known, you can easily obtain V(u). How do you do that?

  Best regards,
  Mario

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