In this chapter we describe a comprehensive set of case studies where gradient projection algorithms are applied to the primal of network design problems. The outcomes are solution methods that provide theoretical support to the design of distributed protocols that optimize resource allocations.
We focus on problems of the form , for which the basic gradient projection iterations are:
We remark that, in order for the gradient iteration (9.1) to inherit the convergence, robustness and stability properties described in Chapter 8, should be a convex set and a convex function, such that the overall problem is convex.
The major difficulty in the application of the gradient scheme (9.1) to the primal problem, is dealing with non-separable feasible sets , for which the projection operation is not easy to compute, or cannot be implemented ...