Resolving the full problem represents a challenging task from a numerical point of view.
A reduced order model, that provides a simplified description of the dynamics of the system, is derived from the full problem using a consistent asymptotic procedure.
It now follows from the regular perturbation structure of the slow flow (4) that if we have a Hopf bifurcation in the reduced problem (5) then it persists generically as a Hopf bifurcation in the full problem (2).
In this context, publications such as [17 23], reporting optimal and suboptimal cross-layer algorithms for very specific wireless multiuser OFDMA network configurations, lack a complete overview of the full problem, making it difficult to extract general conclusions.
The best such subgraph is taken as an approximate optimum for the full problem.
We consider a much simplified version of the full problem.
The numerical algorithm (4.1) is a full linearization problem based on the Newton iterative scheme.
Clearly real-life optimisation would need to take account of many other factors, defined by a full optimisation problem, including mixing, chemical diffusion and thermal diffusion, and energy/efficiency trade-offs.
The conditions given in (2) ensure that problem (3) is a full rank LLS problem.
"It's a big achievement from a group full of problems; problems that look like they will never end," he said as the Chinese Olympic football team were welcomed to their Cobham base for a two-week training camp.
