# Gurobi constraint

**URL:** <https://discourse.julialang.org/t/gurobi-constraint/51798>\
**Category:** Optimization (Mathematical)\
**Tags:** jump, optimization\
**Created:** [December 14, 2020, 10:07am UTC](https://discourse.julialang.org/t/gurobi-constraint/51798 "2020-12-14T10:07:04Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![jay-dave](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jay-dave/32/20269_2.png) [@jay-dave](https://discourse.julialang.org/u/jay-dave)\
**Post date:** [December 14, 2020, 10:07am UTC](https://discourse.julialang.org/t/gurobi-constraint/51798/1 "2020-12-14T10:07:05Z")

</div>

Below is the minimum example of the model I am able to solve. Why is the constraint `@constraint(model, Cost == (x-y)*z)` allowed in Gurobi? Isn’t it nonlinear?

```nohighlight
using JuMP
using Gurobi
model = Model(with_optimizer(Gurobi.Optimizer))
@variable(model, 100>= x >=0)
@variable(model, 100>= y >=0)
@variable(model, z, binary = true)

Cost = @variable(model, Cost)
@constraint(model, Cost == (x-y)*z)
@objective(model, Min, x + Cost)
JuMP.optimize!(model)

```

---

<div class="post-metadata">

**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:** [December 14, 2020, 8:55pm UTC](https://discourse.julialang.org/t/gurobi-constraint/51798/2 "2020-12-14T20:55:19Z")

</div>

Gurobi supports quadratic constraints and objectives. In this case, it is even able to reformulate your model into a mixed-integer linear program. However, Gurobi is still able to solve non-convex quadratic programs. You may be interested in watching [https://www.gurobi.com/resource/non-convex-quadratic-optimization/](https://www.gurobi.com/resource/non-convex-quadratic-optimization/).

p.s. I edited the formatting of your post, you should take a read of [PSA: make it easier to help you](https://discourse.julialang.org/t/psa-make-it-easier-to-help-you/14757).

---

<div class="post-metadata">

**Author:** ![jay-dave](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jay-dave/32/20269_2.png) [@jay-dave](https://discourse.julialang.org/u/jay-dave)\
**Post date:** [December 14, 2020, 8:59pm UTC](https://discourse.julialang.org/t/gurobi-constraint/51798/3 "2020-12-14T20:59:55Z")

</div>

Thank you!