TIAM-MACRO (TM) is a mathematical programming growth model where the global multi-region bottom-up engineering model TIAM is linked with a top-down macroeconomic module MACRO to maximize an inter-temporal utility function for a single representative producer-consumer agent in each region. The size of TM is such that non-linear (NL) optimal solutions cannot be obtained even when the best available personal computers and solvers are used. Therefore, an alternative is proposed based on decomposition methods converting TM to a small-size NL macroeconomic model, called TIAM-MACRO Stand-Alone (TMSA), and where the energy model TIAM is substituted by appropriate quadratic cost-supply functions (QSF). The TIAM model and the TMSA are calibrated to the demands estimated with a scenario generator and are then solved iteratively. This report concentrates on the description and foundation of the algorithm and explains why an adjusted production function is needed to allow for sectoral income and price elasticities that reproduce/calibrate the baseline scenario. It is shown that the decomposed problem for a single region is calibrated and solved to exactly the same results as the original problem in 3 min of computer time instead of 2–3 h without decomposition. Also, for the first time, we are able to solve the global TM model with 15 regions in 1.5 h applying the approach based on TMSA (in Windows 7, 64-bit workstation, solution in a single thread).