# Status of integration, optimization, and nl solvers

**URL:** <https://discourse.julialang.org/t/status-of-integration-optimization-and-nl-solvers/60025>\
**Category:** Numerics\
**Tags:** question\
**Created:** [April 26, 2021, 10:55am UTC](https://discourse.julialang.org/t/status-of-integration-optimization-and-nl-solvers/60025 "2021-04-26T10:55:07Z")\
**Posts on this page:** 1\
**Showing post:** 2

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**Author:** ![Tamas\_Papp](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tamas_papp/32/25949_2.png) [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)\
**Post date:** [April 26, 2021, 11:03am UTC](https://discourse.julialang.org/t/status-of-integration-optimization-and-nl-solvers/60025/2 "2021-04-26T11:03:54Z")

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Depending on your integrals (dimension, smoothness, etc), consider approximating with a Gaussian quadrature, eg as in

> **[GitHub - JuliaApproximation/FastGaussQuadrature.jl: Julia package for Gaussian quadrature](https://github.com/JuliaApproximation/FastGaussQuadrature.jl)**
>
> Julia package for Gaussian quadrature

and from then on you effectively have a sum of function values with (potentially) parameter-dependent weights, in any case it should be easy to handle with any nonlinear solver.

If this is about structural estimation, I recently asked a similar question

> [@Optimization on a manifold](https://discourse.julialang.org/t/optimization-on-a-manifold/59850):
>
> This is both a conceptual question, and a practical one of what packages I could use to solve this. Problem statement I am trying to solve the following problem. Let a \in \mathbb{R}^M be a vector of parameters, and p \in \mathbb{R}^N prices. Market clearing F: \mathbb{R}^M \times \mathbb{R}^N \to \mathbb{R}^N requires that F(a, p) = 0 where F is differentiable in both arguments (both in theory and practice). Take a leap of faith and assume that for each a, there is a unique p(a). I am minim…

and got some good suggestions, which I am working through. Currently I find NLopt (Augmented Lagrangian for the constraint) very robust, but that’s on a toy problem.

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