Based on the NEWUOA algorithm, a new derivative-free algorithm is developed, named LCOBYQA. The main aim of the algorithm is to find a minimizer <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$x^{*} \in\mathbb{R}^{n}$</EquationSource> </InlineEquation> of a non-linear function, whose derivatives are unavailable, subject to linear inequality constraints. The algorithm is...</equationsource></inlineequation>