COBYQA (Constrained Optimisation BY Quadratic Approximations) is an open-source, high-performance derivative-free optimisation solver designed to solve general nonlinear optimisation problems of the form
$$\min_{x \in \mathcal{X}} \quad f(x) \quad \text{s.t.} \quad \begin{cases} b_l \le A x \le b_u, \\ c_l \le c(x) \le c_u, \end{cases}$$
where $\mathcal{X} = \left\{ x \in \mathbb{R}^n : l \le x \le u \right\}$. It was developed to supersede the classical COBYLA algorithm, offering advanced capabilities for handling unconstrained, bound-constrained, linearly constrained, and nonlinearly constrained optimisation tasks using only objective and constraint function values, completely bypassing the need for derivative information.
Key Features Link to heading
- Derivative-Free Trust-Region SQP Method: Utilises a sequential quadratic programming (SQP) framework built on quadratic models from underdetermined interpolation.
- Strict Bound Enforcement: Always respects bound constraints throughout the entire optimisation process, making it ideal for engineering simulations where functions are physically undefined outside target boundaries.
- Comprehensive Constraint Support: Fully handles general linear and nonlinear equality and inequality constraints seamlessly.
Ecosystem Integration Link to heading
COBYQA is a native package in the modern scientific computing landscape. It is integrated directly into the core SciPy library as part of the scipy.optimize module, putting advanced mathematical optimisation directly into the hands of millions of data scientists and engineers worldwide.