A comparative performance analysis for various optimization criterion functions has been carried out for an irreversible Brayton cycle applicable to turbojet engines; the cycle includes the engine core and nozzle and diffuser. Newly defined parameters are introduced as power loss parameter (PLOS), effective power loss parameter (EPLOS) and Carnot-Brayton shape factor (CBSF) for a better assessment of the performance and power losses throughout the operation of the engine cycle. In addition, optimization functions, such as maximum power (MP), maximum power density (MPD), ecological coefficient of performance (ECOP) and ecological function (ECOL) are considered and their optimal operation conditions are compared with respect to each other. Some important evaluations are made for the optimal operation conditions with respect to the ideal Carnot cycle case and also with respect to the ideal Brayton cycle case. Power losses due to internal irreversibilities, as a result of the second law of thermodynamics and due to shape of the cycle model are classified and evaluated. In addition, this paper introduces an assessment of the performance of the turbojet engines in terms of a mass flow rate, gas generator speed and shaft force models as well as considerations for variations of heat leakage. Various parameters affecting the performance analysis are also considered such as compressor pressure ratio theta(c) compressor and turbine efficiencies (eta(c), and eta(t)), respectively), altitude and flight Mach number M-infinity. The comparisons show that the maximum power conditions have the lowest EPLOS but the highest PLOS values with respect to the other optimal function criterions, indicating the effect of the internal irreversibilities at the lowest but exergy destruction for the environment at the highest.