1. Apparatus for optimizing the operating state of a communications network comprising: a plurality of sensors for developing signals representative of present operating state of said network, said signals being related to controllable parameters of said network; first processor, responsive to said sensors, for transforming said signals onto a multi-dimensional space such that said operational state of said communications network is at essentially the center of said multi-dimensional space and said constraints form a polytope in said space; second processor, responsive to said first processor, for computing a path in said space characterized by a power series of order greater than one, along which values of said signals in said space represent a state of said communications network that is monotonically improving with distance from said center; and third processor, reponsive to said second processor, for selecting a point on said curve, developing a modified set of signals corresponding to said selected point and controlling said parameters of said communication network in accordance with said modified set of signals.