# Interior-Point Newton tries points outside of the constraint set

**URL:** <https://discourse.julialang.org/t/interior-point-newton-tries-points-outside-of-the-constraint-set/127215>\
**Category:** New to Julia\
**Tags:** optim, newton, constraint\
**Created:** [March 21, 2025, 10:12am UTC](https://discourse.julialang.org/t/interior-point-newton-tries-points-outside-of-the-constraint-set/127215 "2025-03-21T10:12:23Z")\
**Posts on this page:** 1\
**Showing post:** 2

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**Author:** ![baggepinnen](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/baggepinnen/32/693_2.png) [@baggepinnen](https://discourse.julialang.org/u/baggepinnen)\
**Post date:** [March 21, 2025, 10:31am UTC](https://discourse.julialang.org/t/interior-point-newton-tries-points-outside-of-the-constraint-set/127215/2 "2025-03-21T10:31:21Z")

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I’m not sure how Optim’s interior-point method works, but you might find this post informative

> [@OptimizationMOI Ipopt violating inequality constraint](https://discourse.julialang.org/t/optimizationmoi-ipopt-violating-inequality-constraint/92608/2):
>
> That is a frequent misconception. If a problem has a constraint g(x) \leq 0, for an interior-point method to ensure satisfaction of the constraint throughout, it would have to penalize g(x) in the logarithmic barrier. However, that’s not what IPOPT does. Firstly, IPOPT adds slack variables s to transform the constraint to g(x) + s = 0 and s \geq 0. Secondly, the inequality on s is penalized via the log barrier, i.e., s \> 0 (strictly) is maintained throughout. BUT g(x) + s = 0 is NOT maintained…

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