# Log determinant objective

**URL:** <https://discourse.julialang.org/t/log-determinant-objective/23927>\
**Category:** Optimization (Mathematical)\
**Created:** [May 6, 2019, 7:31pm UTC](https://discourse.julialang.org/t/log-determinant-objective/23927 "2019-05-06T19:31:27Z")\
**Posts on this page:** 1\
**Showing post:** 6

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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:** [December 16, 2021, 9:49pm UTC](https://discourse.julialang.org/t/log-determinant-objective/23927/6 "2021-12-16T21:49:32Z")

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> How does one use this?

Here’s an example, but it isn’t supported by Ipopt or NLopt, you’ll need to reformulate your entire problem as a conic optimization problem and use a solver like Mosek or SCS.

> **[Standard form · MathOptInterface](https://jump.dev/MathOptInterface.jl/stable/reference/standard_form/#MathOptInterface.LogDetConeSquare)**
>
> Documentation for MathOptInterface.

```julia
# max log(det(x))
#
# is equivalent to
# max t
# s.t. t <= log(det(X))

model = Model()
@variable(model, X[1:3, 1:3])
@variable(model, t)
@constraint(model, [t; 1; vec(X)] in MOI.LogDetConeSquare(3))
@objective(model, Max, t)

```

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