Several computational techniques to optimize the performance measure of linear state-regulator problems are thoroughly investigated. These techniques possess the central notions of multilevel decomposition-coordination procedures and are divided into four basic categories with each category containing two alternative methods. It has been proved from the coordinability standpoint that the optimization techniques of three categories are dual pairs. Structural properties as well as the main advantages and limitations of the various methods are carefully pointed out in order to evaluate their range of practicality. For the different two-level control structures developed in this work, the concept of system coordinability is elegantly related to the system functional controllability and observability concepts.