Performance of linear Fresnel collectors may largely depend on the secondary-reflector profile design when small-aperture absorbers are used. Optimization of the secondary-reflector profile is an extremely challenging task because there is no established theory to ensure superior performance of derived profiles. In this work, an innovative optimization method is proposed to optimize the secondary-reflector profile of a generic linear Fresnel configuration. The method correctly and accurately captures impacts of both geometric and optical aspects of a linear Fresnel collector to secondary-reflector design. The proposed method is an adaptive approach that does not assume a secondary shape of any particular form, but rather, starts at a single edge point and adaptively constructs the next surface point to maximize the reflected power to be reflected to absorber(s). As a test case, the proposed optimization method is applied to an industrial linear Fresnel configuration, and the results show that the derived optimal secondary reflector is able to redirect more than 90% of the power to the absorber in a wide range of incidence angles. The proposed method can be naturally extended to other types of solar collectors as well, and it will be a valuable tool for solar-collector designs with a secondary reflector. (C) 2017 Elsevier Ltd. All rights reserved.