UOBYQA

UOBYQA (Unconstrained Optimization BY Quadratic Approximation) is a numerical optimization algorithm by Michael J. D. Powell. It is also the name of Powell's Fortran 77 implementation of the algorithm.

UOBYQA solves unconstrained optimization problems without using derivatives, which makes it a derivative-free algorithm. The algorithm is iterative and exploits trust-region technique. On each iteration, the algorithm establishes a quadratic model ${\displaystyle Q_{k}}$ by interpolating the objective function at ${\displaystyle (n+1)(n+2)/2}$ points and then minimizes ${\displaystyle Q_{k}}$ within a trust region.

...
Wikipedia