COBYQA

Constrained Optimization BY Quadratic Approximations, also known as COBYQA, is a gradient-free optimization algorithm developed to improve upon the COBYLA algorithm. COBYQA employs a derivative-free, trust-region SQP approach, utilizing quadratic models derived from underdetermined interpolation. Unlike COBYLA, COBYQA also supports equality constraints and can handle general nonlinear optimization problems.

Note

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.

Before using the COBYQA solver in modOpt, ensure that you have the cobyqa optimizer installed.

Warning

cobyqa is available with scipy>=1.14.0 which requires python>=3.10.0. If your machine does not satisfy these requirements, install the ‘cobyqa’ package by running pip install cobyqa.

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

from modopt import COBYQA

Options could be set by just passing them within the solver_options dictionary when instantiating the COBYQA optimizer object. For example, we can set the maximum number of function evaluations maxfev and the tolerance on the maximum constraint violation feasibility_tol as shown below.

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

The options available for the COBYQA solver in modOpt are given in the following table. For more information on the COBYQA algorithm and for advanced options, visit COBYQA documentation.

COBYQA solver options
Option	Type (default value)	Description
`maxfev`	int (`500`)	Maximum number of function evaluations.
`maxiter`	int (`1000`)	Maximum number of iterations.
`target`	float(`-np.inf`)	Target value for the objective function. Terminate succesfully if the objective function value of a feasible point `xk` (see `feasibility_tol` below) is less than or equal to `target`, i.e., `f(xk)<=target`.
`feasibility_tol`	float (`1e-8`)	Tolerance on the maximum constraint violation. A point is considered feasible if the maximum constraint violation at a point is less than or equal to this `feasibility_tol`.
`radius_init`	float (`1.0`)	Initial trust region radius. Typically, this value should be in the order of one tenth of the greatest expected change to `x0`.
`radius_final`	float (`1e-6`)	Final trust region radius. Specifies the accuracy needed in the final values of the variables.
`nb_points`	int (`2*n+1`)	Number of interpolation points used to build the quadratic model of the objective and constraint functions. Must satisfy `0<nb_points<=(n+1)*(n+2)//2`, where `n=len(x)`.
`scale`	bool (`False`)	Set to `True` to scale the variables according to the bounds. If `True` and if all the lower and upper bounds are finite, the variables are scaled to be within the range `[-1,+1]`. If any of the lower/upper bounds is infinite, the variables are not scaled.
`filter_size`	int (`1e6`)	Maximum number of points in the filter. The filter is used to select the best point returned by the optimization procedure.
`store_history`	bool (`False`)	Set to `True` to store the history of the objective function values and maximum constraint violations.
`history_size`	int (`1e6`)	Maximum number of function evaluations to store in the history.
`debug`	bool (`False`)	Set to `True` to perform additional checks during optimization. Should be used only for debugging purposes and is not recommended for general users.
`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.