Chapter 9Primal Gradient Algorithms

9.1 Introduction

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 c9-math-0001, 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, c9-math-0003 should be a convex set and c9-math-0004 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 c9-math-0005, for which the projection operation c9-math-0006 is not easy to compute, or cannot be implemented ...

Get Optimization of Computer Networks now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.