NelderMead

The Nelder-Mead simplex algorithm is a local search, gradient-free optimization algorithm. This solver uses the ‘Nelder-Mead’ algorithm from the Scipy library.

Note

NelderMead can solve only bound-constrained problems. Please use other gradient-free algorithms such as COBYLA or COBYQA if your problem has constraints other than simple variable bounds. For better efficiency, we recommend using general nonlinear programming algorithms such as PySLSQP or IPOPT if first order derivative information is available for the objective and constraints of your problem.

To use the NelderMead solver, start by importing it as shown in the following code:

from modopt import NelderMead

Options could be set by just passing them within the solver_options dictionary when instantiating the NelderMead optimizer object. For example, we can set the maximum number of function evaluations maxiter and the minimum absolute error in x_best between iterations xatol as shown below.

optimizer = NelderMead(prob, solver_options={'maxiter':1000, 'catol':1e-6})

The options available for the NelderMead solver in modOpt are given in the following table. For more information on the Scipy ‘Nelder-Mead’ algorithm, visit Scipy documentation.

NelderMead solver options
Option	Type (default value)	Description
`maxfev`	int (`1000`)	Maximum number of function evaluations.
`maxiter`	int (`1000`)	Maximum number of iterations. The optimization will stop as soon as either of `maxfev` or `maxiter` is reached.
`xatol`	float (`1e-4`)	Terminate if absolute error in `x_best` between iterations is less than `xatol`.
`fatol`	float (`1e-4`)	Terminate if absolute error in `f(x_best)` between iterations is less than `fatol`. For convergence, both `xatol` and `fatol` need to be satisfied.
`adaptive`	bool (`False`)	Set to `True` to adapt algorithm parameters to the dimensionality of the problem. Useful for high-dimensional problems.
`initial_simplex`	np.ndarray (`None`)	Initial simplex coordinates of shape `(n+1,n)`where `n=len(x)`. If given, overrides `x0`. `initial_simplex[j,:]` should contain the coordinates of the j-th vertex of the `n+1` vertices of the simplex.
`return_all`	bool (`False`)	Set to `True` to return a list containing the best solution from each iteration in the final results dict.
`disp`	bool (`False`)	Set to `True` to print convergence messages. If `False`, no console outputs will be generated.
`callback`	callable (`None`)	Function to be called after each iteration. The function is called as `callback(xk, fk)`, where `xk` is the optimization variable vector from the current iteration, and `fk` is the corresponding objective value.