This code randomly generates quadratic max-min optimization problems of 
the form

     min  1/2 x^TQx+qx
     s.t. max_{1<=j<=r} min_{i /in N_j} a_{ij}x+b_{ij}<=0

and solves them with the decomposition method explained in section 6 of the 
paper S.Scholtes (2002), Combinatorial Structures in Nonlinear Programming, 
downloadable at www.eng.cam.ac.uk/~ss248/publications/scholtes_2002.pdf.

It consists of the files 

gen.m    - random problem generator
qpqp.m   - solver
testqp.m - control for sample of tests

In order to use the code you need to save the files gen.m qpqp.m testqp.m 
in a directory and add this directory to your matlab path. 

To initialise the test runs you need to set at the Matlab prompt the 
following parameters: 

n= (number of variables), 
m= (number of selection functions), 
l= (number of min functions in max-min expression),
t= (number of test problems)

Then type testqp and the program will output the successive results of the 
QP iterations. It will also generate two arrays. The array Vqp keeps track 
of the first and last objective function value and the array Itqp tracks 
the number of QP iterations used until a stationary point was found. 

This implementation is considerably slower than the version with the
Dundee QP solver "BQPD" which has nice warm start properties. A replacement
file for qpqp which makes use of this code is available on request but 
requires that you have the BQPD solver linked to your Matlab code. 

You may wish to change the qpqp.m file to take advantage of warm 
starting of the qp solver. Also, if you are infeasible initially 
(can happen if m,l are much larger than n), then the Dundee solver 
generates automatically a feasible problem (or at least attempts to do so). 
The matlab QP solver seems to be making progress then as well but I can't 
explain why because I don't know how the solver works. An alternative 
is to use a phase-1 approach as indicated in the paper.

The Matlab QP solver is known to be unreliable if the Hessian of the
objective function is not positive definite. This should not be a problem
here since the generator gen.m generates problems with positive definite
Hessians.