An inverse space mapping optimization algorithm for designing linear and non-linear microwave circuits is presented in this work for the first time. The inverse space mapping follows a piece-wise linear formulation, avoiding the use of neural networks. Microwave circuits in the frequency domain or in the time domain transient-state can be efficiently optimized by applying this algorithm. We contrast our new algorithm with Neural Inverse Space Mapping (NISM) optimization. The physical design of a set of CMOS inverters driving an electrically long microstrip line on FR4 illustrates our algorithm.