COBYLA

Constrained Optimization BY Linear Approximation, also known as COBYLA, is a gradient-free optimization algorithm. This solver uses the ‘COBYLA’ algorithm from the Scipy library.

Note

COBYLA cannot solve problems with equality constraints. Please use other gradient-free algorithms such as COBYQA if your problem has equality constraints. 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 COBYLA solver, start by importing it as shown in the following code:

from modopt import COBYLA

Options could be set by just passing them within the solver_options dictionary when instantiating the COBYLA optimizer object. For example, we can set the maximum number of iterations maxiter and the absolute tolerance for the constraint violations catol as shown below.

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

A limited number of options are available for the COBYLA solver in modOpt as given in the following table. For more information on the Scipy ‘COBYLA’ algorithm, visit Scipy documentation.

COBYLA solver options
Option	Type (default value)	Description
`maxiter`	int (`1000`)	Maximum number of function evaluations.
`rhobeg`	float(`1.0`)	Reasonable initial changes to the variables.
`tol`	float (`1e-4`)	Final accuracy in the optimization (not precisely guaranteed). This is a lower bound on the size of the trust region.
`catol`	float (`2e-4`)	Absolute tolerance for the constraint violations.
`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)`, where `xk` is the optimization variable vector from the current iteration.