How to call the gradient-based algorithm when the objective function and the gradient's formulas are obtained?

Question

I use the fenics to solve an optimization problem. The problem is like:

objective function: x^2+y^2.

Then, I can obtain the gradient of objective function corresponding to the variables x and y,

Gradient formulas: 2x and 2y

The problem is: how to call the gradient-based algorithm when the objective function and the gradient's formulas are obtained in fenics?

In fact, the optimization problem I face is far more difficult than this problem. Moreover, I am familiar with optimization process as follows

# Solve the Navier-Stokes equations
solve(F == 0, s, bcs=bcu+bcp)

# Define the optimisation proble,
alpha = Constant(1e-4)
J = Functional(inner(grad(u), grad(u))*dx + alpha*inner(f,f)*dx)
m = InitialConditionParameter(f)
rf = ReducedFunctional(J, m)

# Solve the optimisation problem
m_opt = minimize(rf, method="Newton-CG", tol=1e-8)

# Plot the optimised results
f.assign(m_opt)
solve(F == 0, s, bcs=bcu+bcp)

But, this case is different from my question because the gradient formula is given by "ReducedFunctional" while I can obtain the gradient formula by other computations.

Comments

You can try to use the minimize function in scipy in stead, see e.g here: https://docs.scipy.org/doc/scipy/reference/tutorial/optimize.html