# COBYLA

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Constrained optimization by linear approximation (COBYLA) is a numerical optimization method for constrained problems where the derivative of the objective function is not known, invented by Michael J. D. Powell. That is, COBYLA can find the vector ${\displaystyle {\vec {x}}\in {\mathcal {S}}}$ with ${\displaystyle {\mathcal {S}}\subseteq \mathbb {R} ^{n}}$ that has the minimal (or maximal) ${\displaystyle f({\vec {x}})}$ without knowing the gradient of ${\displaystyle f}$. COBYLA is also the name of Powell's software implementation of the algorithm in Fortran.[1]
Powell invented COBYLA while working for Westland Helicopters.[2] It proceeds by iteratively approximating the actual objective function ${\displaystyle f}$ with linear programs.