This article introduces a new concept of solution of a linear singular system (descriptor system), based on minimization. It is shown that, by imposing a hypothesis on the matrices of the descriptor system, the minimization-based solution exists and is unique for any initial condition. In particular, if the initial condition is consistent, then the minimization-based solution is equal to the classical solution. Also in this work, a numerical example is given in order to analyze the minimization-based solutions for different initial conditions.