COBYQA documentation#



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Tom M. Ragonneau | Zaikun Zhang

COBYQA is a derivative-free optimization solver designed to succeed COBYLA. Using only functions values, and no derivatives, it aims at solving problems of the form

\[\begin{split}\min_{x \in \xbd} \quad \obj ( x ) \quad \text{s.t.} \quad \begin{cases} \aub x \le \bub, ~ \aeq x = \beq,\\ \cub ( x ) \le 0, ~ \ceq ( x ) = 0, \end{cases}\end{split}\]

where \(\xbd = \{ x \in \R^n : \xl \le x \le \xu \}\). COBYQA always respect the bound constraints throughout the optimization process. Hence, the nonlinear functions \(\obj\), \(\cub\), and \(\ceq\) do not need to be well-defined outside \(\xbd\). In essence, COBYQA is a derivative-free trust-region SQP method based on quadratic models obtained by underdetermined interpolation. For a more detailed description of the algorithm, see the framework description.

To install COBYQA, run in your terminal

pip install cobyqa

For more details on the installation and the usage of COBYQA, see the user guide.

Citing COBYQA#

If you would like to acknowledge the significance of COBYQA in your research, we suggest citing the project as follows.

The corresponding BibTeX entries are given hereunder.

    author          = {Ragonneau, T. M.},
    title           = {Model-Based Derivative-Free Optimization Methods and Software},
    school          = {Department of Applied Mathematics, The Hong Kong Polytechnic University},
    address         = {Hong Kong, China},
    year            = 2022,

    author          = {Ragonneau, T. M. and Zhang, Z.},
    title           = {{COBYQA}: {C}onstrained {O}ptimization {BY} {Q}uadratic {A}pproximations},
    howpublished    = {Available at},
    note            = {Version 1.0.0},
    year            = 2023,


As of December 08, 2023, COBYQA has been downloaded 2,062 times, including


The early development of COBYQA was funded by the University Grants Committee of Hong Kong, under the Hong Kong PhD Fellowship Scheme (ref. PF18-24698). It is now supported by The Hong Kong Polytechnic University.