# Add lower bound to objective function?
**URL:** https://discourse.julialang.org/t/add-lower-bound-to-objective-function/36261
**Category:** Optimization (Mathematical)
**Created:** [March 20, 2020, 1:12pm UTC](https://discourse.julialang.org/t/add-lower-bound-to-objective-function/36261 "2020-03-20T13:12:24Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@gobs](https://discourse.julialang.org/u/gobs)
#### Post date: [March 20, 2020, 1:12pm UTC](https://discourse.julialang.org/t/add-lower-bound-to-objective-function/36261/1 "2020-03-20T13:12:24Z")
I would like to help the MILP solver used by JuMP by providing it with a lower bound on the objective function. Is there a “smart” way of doing this other than to just add a constraint to the objective fcn expression, e.g. a function that does something like `set_lower_bound(JuMP.Model)`?
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### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [March 20, 2020, 4:06pm UTC](https://discourse.julialang.org/t/add-lower-bound-to-objective-function/36261/2 "2020-03-20T16:06:31Z")
A better way to help the solver is to provide a good starting solution: [Variables · JuMP](https://www.juliaopt.org/JuMP.jl/stable/variables/#Start-values-1).
JuMP does not provide a solver-independent way to tell solvers a lower bound on the objective. In general, (if minimizing) lower bounds aren’t very helpful. Good _upper_ bounds are though.
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### Author:  [@ccoffrin](https://discourse.julialang.org/u/ccoffrin)
#### Post date: [March 20, 2020, 6:31pm UTC](https://discourse.julialang.org/t/add-lower-bound-to-objective-function/36261/3 "2020-03-20T18:31:28Z")
A general way of communicating an objective bound to many solvers is to add it as a constraint. So you might give that a try.
In my experience (assuming a minimization problem), providing lower bounds as constraints is not particularly helpful. However, providing strong objective upper bounds as constraints can be very helpful.
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### Author:  [@gobs](https://discourse.julialang.org/u/gobs)
#### Post date: [March 20, 2020, 6:31pm UTC](https://discourse.julialang.org/t/add-lower-bound-to-objective-function/36261/4 "2020-03-20T18:31:48Z")
Thanks! I can do both, but from what I’ve gathered from my problem is that the solver needs a better lower bound in order to cut off branches in the branch and bound tree. It finds a good solution fairly qucikly, but then spends a lot of time bringing the lower bound up in order to decrease the optimality gap. I might be mixing up lower and upper bounds (I’m minimising).
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### Author:  [@WalterMadelim](https://discourse.julialang.org/u/WalterMadelim)
#### Post date: [April 24, 2025, 2:36am UTC](https://discourse.julialang.org/t/add-lower-bound-to-objective-function/36261/5 "2025-04-24T02:36:34Z")
FWIW, here is a related reference [arXiv:2301.13149v2](https://arxiv.org/abs/2301.13149v2)