// @ Author : Zheng MA, zhengma@cs.yale.edu
// @ Home: http://www.cs.yale.edu/~zhengma
// @ Date : 11/12/2002


This is a simple working version of the solver for 
System Optimization Flow assignment problem and
the 
User(selfish) Optimization Flow assignment problem(Nash Equilibrium).

In this solver, I use an exsiting a matlab program called "Primal-Dual method for
solving seperable convex optimization problem(PDSOC.m)" from SOL @Stanford University,
(All rights reserved for their own, see: http://www.stanford.edu/group/SOL/software.html)
which can solve a nonlinear convex optimization problem:

min sum_i f(x_i), f is convex possibly nonlinear
given Ax=b. (A is sparse, m*n matrix)

I reformulate the System optimization flow assignment problem and
the selfish user optimization flow assignment problem to the format above.
In my formulation, basically x(vector) represent 
all the edges and possible paths for the O-D pairs in the graph.

MatrixGen.java assign variables to each edge and path for 
the O-D pairs and generate the proper matrix A and
vector b. 

You can just type "test" in matlab to see the result for an example
in the book:"Handbooks in OR & MS vol.8, Chapter6 Network Equilibrium Models and 
Algorithms" page 488. I have input the graph in fig1 according my topology format
in "test.top". The "test.m" is the main entry for the whole progrm, you need to
change input file name for matrix A and vector b, and the latency file as well.

The argument you need to change by hand for a new graph are following:
Suppose f(x) is the latency function of an edge. x is the current aggregate traffic

sysFun.m: xf(x)
sysGrad.m: (xf(x))'
sysHess.m: (xf(x))''

usrFun.m:  F(x)=$f(t)dt (integral of f(t) at x)
usrGrad.m: f(x)=(F(x))'
usrHess.m: (f(x))'

Note: those six functions can take two arguments, bandwidth of an edge u and current traffic x

You may also need to tune the argument in "test.m" for the PDSCO algorithm like the initial 
value of x,z(solution for dual problem) to make the algorithm converge.