The sequential quadratic programming (SQP) algorithm is applied to reconstruct the time- and space-dependent boundary conditions in 1D and 2D radiative-conductive systems in this study. The coupled radiation-conduction heat transfer in absorbing, scattering and emitting media is solved by the discrete ordinate method combined with finite volume method, and the simulated boundary temperature is served as input for the inverse analysis. The SQP algorithm is employed as the optimization technique, through which the time-dependent boundary heat flux in 1D heat transfer problems and the space dependent boundary heat flux and convective heat transfer coefficient in 2D heat transfer problems are recovered. No prior information on the functional forms of the unknown boundary conditions is needed for inverse analysis. All the retrieval results show that the SQP algorithm is robust to the reconstruction of thermal boundary conditions in coupled radiative-conductive systems. The present inverse technique is proved to be more efficient and accurate than the conjugate gradient method, Levenberg-Marquardt method and particle swarm optimization algorithm. (C) 2019 Elsevier Ltd. All rights reserved.