# Can Ipopt provide a dual bound?

**URL:** <https://discourse.julialang.org/t/can-ipopt-provide-a-dual-bound/128354>\
**Category:** Optimization (Mathematical)\
**Tags:** question, ipopt\
**Created:** [April 24, 2025, 6:48am UTC](https://discourse.julialang.org/t/can-ipopt-provide-a-dual-bound/128354 "2025-04-24T06:48:35Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![WalterMadelim](https://avatars.discourse-cdn.com/v4/letter/w/3e96dc/32.png) [@WalterMadelim](https://discourse.julialang.org/u/WalterMadelim)\
**Post date:** [April 24, 2025, 6:48am UTC](https://discourse.julialang.org/t/can-ipopt-provide-a-dual-bound/128354/1 "2025-04-24T06:48:35Z")

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Continuing the discussion from [Getting duals for nonlinear programming problem](https://discourse.julialang.org/t/getting-duals-for-nonlinear-programming-problem/11357):

As an extension, I asked ChatGPT this problem.

 ![image](https://global.discourse-cdn.com/julialang/original/3X/4/b/4b9a98514e6913a26c355c1c8d8e9b382334ca41.png)

Can anyone tell me where is its idea from? Does its reply make sense?

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**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [April 24, 2025, 6:50am UTC](https://discourse.julialang.org/t/can-ipopt-provide-a-dual-bound/128354/2 "2025-04-24T06:50:57Z")

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It does not make sense. Ipopt cannot provide a global dual bound.

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**Author:** ![WalterMadelim](https://avatars.discourse-cdn.com/v4/letter/w/3e96dc/32.png) [@WalterMadelim](https://discourse.julialang.org/u/WalterMadelim)\
**Post date:** [April 24, 2025, 6:57am UTC](https://discourse.julialang.org/t/can-ipopt-provide-a-dual-bound/128354/3 "2025-04-24T06:57:46Z")

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I agree.

Here are my thoughts:  
If the primal problem is a Min problem, then the dual problem is a Max-Min problem.  
A dual bound can typically be obtained at a dual feasible point (e.g. `μ_0`).  
However, this entails an exact (i.e. global) Minimization subprocedure.  
If this (simpler) subprocedure itself doesn’t admit a global solution, a valid dual bound can not be derived.