Accelerated Dual Descent for Network Optimization
For distributed network optimization, this provides a practical acceleration of dual descent while preserving distributed implementation, though the approach is incremental (combining Newton approximations with dual descent).
Dual descent methods for network optimization are slow; this paper accelerates them using approximate Newton directions computed via local information exchanges, achieving superlinear convergence and 10-100x faster convergence than existing distributed methods.
Dual descent methods are commonly used to solve network optimization problems because their implementation can be distributed through the network. However, their convergence rates are typically very slow. This paper introduces a family of dual descent algorithms that use approximate Newton directions to accelerate the convergence rate of conventional dual descent. These approximate directions can be computed using local information exchanges thereby retaining the benefits of distributed implementations. The approximate Newton directions are obtained through matrix splitting techniques and sparse Taylor approximations of the inverse Hessian.We show that, similarly to conventional Newton methods, the proposed algorithm exhibits superlinear convergence within a neighborhood of the optimal value. Numerical analysis corroborates that convergence times are between one to two orders of magnitude faster than existing distributed optimization methods. A connection with recent developments that use consensus iterations to compute approximate Newton directions is also presented.