The first part of this paper considers the computer-aided design of multivariable structurally constrained regulators for linear time-invariant plants. Two relevant control problems which can be effectively solved by a parameter optimisation approach, are introduced; the basic role played by the internal model principle is then specifically pointed out, and the reformulation of the resulting optimisation problems as mathematical programs are given. The most relevant aspects of the computational algorithms developed to solve these problems are finally outlined, along with the main features of the program package developed to solve, among others, the two cases presented in Part 2