software project: The theory of duality (optimization lab)

This project involves applying the primal-dual algorithm of nonlinear programming to minimize a given objective function subject to equality constraints. The algorithm involves two stages, where the first stage involves optimizing for the primal problem with fixed Lagrange multipliers, and the second stage involves optimizing for the dual problem with fixed primal solutions. The algorithm terminates when a satisfactory solution is found. The project includes an example problem with a specific objective function and constraint set, and the project implementation requires the implementation of the functions PhiL(λ), and PhiX(x) and integrating them into the primal-dual algorithm scheme. The project assumes that the functions involved are convex, and high accuracies may be challenging to achieve using this method.
you can make this project in language c or c++