Development of a R code to solve a large system of equations with linear constrains

Our project team is aimed at providing data analysis to the rest of the company to make data-driven decisions. We faced a problem when we discovered that the Excel solver was not able to solve some “large” problem. So we switched to R and our first tests are quite encouraging. Now we need some support and some consulting in order to use it efficiently and to industrialize our approach.
The Data Analyst can be a freelance and will be in charge of the R part of the project and the automation of the process. He will collaborate with Business and IT teams to develop the most efficient approach to solve this multi-variables problem.

Context
For business purpose, I need to solve every month some large systems of equations with constrains.
– X can have n variables (n between 1000 and 4000 variables)
– f(X) Rn -> R is known and can even be improved by the Data analyst. It is not a linear function.
– grad(f) has been calculated.
– constrains are linear. The inequalities are written in R such that: Amat %*% X >= b (Amat a matrix and b, a vector, are given).
I tried to find a minimum using the BBoptim from the “BB” library. It almost works with n = 600. Not so quickly. But I’m just a novice with R.

Location
The job can be done working from home. Nonetheless if the consultant is based in Europe and even in France, it could be an advantage for teamwork.

Job content
Identify relevant algorithms and processes to solve/find a minima for a “large” problem of inequation.
Code identified algorithm
Quantify effectiveness of algorithms
Propose and implement some improvements
Document process, code, remarks

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