Optomechanical cooling is a prerequisite for many exotic applications promised by modern quantum technology and it is crucial to achieve it in short times, to minimize the undesirable effects of the environment. We formulate cavity optomechanical cooling as a minimum-time optimal control problem on anti-de Sitter space of appropriate dimension and use the Legendre pseudospectral optimization method to estimate the minimum time and the corresponding optimal control, for various values of the maximum coupling rate between the cavity field and the mechanical resonator. This framework can also be applied for the fast creation of optomechanical entanglement and to improve the efficiency of an optomechanical quantum heat engine. (C) 2016 Elsevier Ltd. All rights reserved.