autopdex.solver.solve_nonlinear_minimization

autopdex.solver.solve_nonlinear_minimization(dofs, settings, static_settings, **kwargs)

Solves a nonlinear minimization problem using specified optimization methods.

This function wraps nonlinear minimization solvers provided by jaxopt to minimize a functional and solve the given problem.

Parameters:

• dofs (jnp.ndarray or dict) – Degrees of freedom or initial guess for the solution.

• settings (dict) – Dictionary containing various settings and parameters required for assembling the problem.

• static_settings (dict) – Dictionary containing static settings such as solver type, verbose level, and variational schemes.

• **kwargs (dict) – Additional keyword arguments passed to the specific solver functions.

Returns:

The optimized solution obtained from the selected solver.

Return type:

jnp.ndarray

Solver Types

• ‘gradient descent’ : Uses gradient descent for optimization.

• ‘lbfgs’ : Uses Limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm for optimization.

• ‘bfgs’ : Uses Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm for optimization.

• ‘nonlinear cg’ : Uses nonlinear conjugate gradient method for optimization.

• ‘gauss newton’ : Uses Gauss-Newton method for optimization.

• ‘levenberg marquart’ : Uses Levenberg-Marquardt algorithm for optimization.

• Default : If solver name is not set or not available, uses ‘lbfgs’ as the default solver.

Notes

• This function should just be called, if the variational scheme involves the definition of a functional that is to be minimized, e.g. ‘least square pde loss’. The modes ‘gauss newton’ and ‘levenberg marquart’ are an exeption, since they utilize the residual.

• The function conducts the assembler.integrate_functional and assembler.assemble_residual functions in order to set up suitable optimization functions or residual functions, depending on what the solver needs.

• The current implementation does not support nodal imposition of DOFs.