This paper reports a computational optimization study for an inverse z-pinch magnetized target fusion system (MTF). This has been carried out by varying various parameters such as the magnetizing current, the initial liner radius and thickness, liner length, etc. One-dimensional (1D) magneto-hydrodynamic (MHD) calculations are used for this purpose. Capacitor bank parameters are held constant, as is also the inner conductor radius. The Kadomtsev stability parameter Q₀ is kept constant at 0.9 and the maximum plasma β at 0.4. The optimization study has yielded several parametric sets with an energy gain of more than unity, i.e. fusion energy output that exceeds the initial energy in the capacitor bank. A physical explanation for the local optimal points is provided through an energy flow analysis. For one case with energy gain exceeding unity, a simple liner stability analysis has been performed. This involves analytical calculations of the time points at which different liner modes become unstable. For these analytical studies, time-dependent parameters, such as liner acceleration, effective thickness of the liner region that still remains solid, and effective material strength, are obtained from 1D MHD simulations.