COBYQA documentation#

Version: 1.0.dev1

Useful links: Issue tracker | Mailing list

COBYQA is a derivative-free solver for general nonlinear optimization. It aims at solving problems of the form

\[\begin{split}\min_{x \in \R^n} f(x) \quad \text{s.t.} \quad \left\{ \begin{array}{l} g(x) \le 0,\\ h(x) = 0,\\ l \le x \le u, \end{array} \right.\end{split}\]

where \(f\) is a real-valued objective function, \(g\) and \(h\) are vector-valued constraint functions, and \(l\) and \(u\) are vectors of lower and upper bounds on the variables \(x\). COBYQA uses function values of \(f\), \(g\), and \(h\), but no derivatives. It also assumes that the bound constraints are inviolable and always respect them.


This section provides detailed mathematical descriptions of the algorithms underneath COBYQA.

To the algorithm descriptions

API reference

This section references an exhaustive manual detailing the functions, modules, and objects included in COBYQA.

To the reference guide

COBYQA aims at being a modern successor of the well-known solver COBYLA.


As of June 01, 2023, COBYQA has been downloaded 1353 times (mirror downloads excluded).

Citing COBYQA#

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

The corresponding BibLaTeX entries are given hereunder.

    author      = {Ragonneau, T. M.},
    title       = {Model-Based Derivative-Free Optimization Methods and Software},
    type        = {phdthesis},
    institution = {Department of Applied Mathematics, The Hong Kong Polytechnic University},
    location    = {Hong Hong},
    date        = {2022},

    author       = {Ragonneau, T. M. and Zhang, Z.},
    title        = {{COBYQA}: Constrained Optimization BY Quadratic Approximations},
    url          = {},
    version      = {1.0.dev1},
    date         = {2023},


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