COBYQA

Mon, 13 Jul 2026 00:00:00 +0000

COBYQA (Constrained Optimization BY Quadratic Approximations) is an open-source, high-performance derivative-free optimization solver designed to solve general nonlinear optimization 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 optimization tasks using only objective and constraint function values, completely bypassing the need for derivative information.

PDFO

Mon, 13 Jul 2026 00:00:00 +0000

PDFO (Powell’s Derivative-Free Optimization solvers) is an open-source, high-performance interface that wraps the legendary derivative-free optimization solvers developed by Professor M. J. D. Powell. Rather than a reimplementation, PDFO serves as a cross-platform wrapper around the original, highly optimized Fortran backends, making them natively accessible to modern computing environments.

PDFO aims at solving general nonlinear optimization problems of the form:

$$\min_{x \in \mathcal{X}} \quad f (x)$$

where the constraints defining the feasible set $\mathcal{X} \subseteq \mathbb{R}^n$ depend entirely on the underlying Powell solver selected to execute the task:

Tom Ragonneau

COBYQA

PDFO