COBYQA documentation#



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Tom M. Ragonneau | Zaikun Zhang

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

\[\begin{split}\min_{x \in \R^n} \quad \obj ( x ) \quad \text{s.t.} \quad \left\{ \begin{array}{l} \xl \le x \le \xu,\\ \aub x \le \bub, ~ \aeq x = \beq,\\ \cub ( x ) \le 0, ~ \ceq ( x ) = 0. \end{array} \right.\end{split}\]

COBYQA assumes that the bound constraints \(l \le x \le u\) are unrelaxable, i.e., that the nonlinear functions \(\obj\), \(\cub\), and \(\ceq\) cannot be evaluated outside the bounds. Hence, COBYQA always respect the bound constraints throughout the optimization process. To install COBYQA, run in your terminal

pip install cobyqa

For more details, 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 September 28, 2023, COBYQA has been downloaded 1,638 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.