### Homework 2, due Feb 10:

Experiment with Vanderbei's
Simplex Pivot Tool . Use this link (not the one from the text book
home page), with the default values for rows (*m*), cols (*ntilde*),
seed (which defines the random number generator), and the number of
problems (10). Include the grader's email address (yangxi@cims.nyu.edu)
so he is informed of your scores. You may exit and restart at any time.

Verify that my Matlab code simplx.m (see course home page) generates
the same answers as the Simplex Pivot Tool, provided you use the same
strategy to choose the entering and leaving variables in both cases.
In particular, verify that the dictionary is the same at every step
(make sure the definitions of * y * and * BinvN* do
not have semicolons so their output is not suppressed).
You need to press any key to continue after the message about which
variables enter and leave the basis.
If the dictionaries differ from those generated by the Simplex Pivot Tool,
probably you are doing something wrong: come and see me.
You do not need to test all the problems; just run enough to convince
yourself and provide evidence that this is the case (a few pages of output,
not too much). To get output from a Matlab session, type * help diary *.
Before calling the script * simplx *, you need to define the
quantities * Atilde, b, ctilde * and * maxit *.
To find out how to set up a matrix in Matlab, type * help paren *.
For more information on Matlab, see the course home page.

Modify the Matlab code so that it keeps track of what variables are
in the basis: at present, it computes the optimal value of the LP but does
not keep track of which of the original variables (regular or slack) are
in the basis and which are not. Hint: start by setting two vectors
* nonbasics = 1 : m * (the vector [1 2 3....m])
and * basics = ntilde + 1: ntilde + m * ,
and change these appropriately at each iteration, making sure that the
ordering corresponds to the ordering in the columns of * B * and * N* .
Check that the updated values agree with those generated by the
Simplex Pivot Tool, remembering that * w_j * is the same as * x_(ntilde + j)* . Turn in a program listing highlighting the change you made
together with evidence that it works correctly.

The harder problem of changing the code to use the simple updating
explained in Chapter 1 instead of the overkill of the "backslash"
opertor to compute * B^(-1) N* and * B^(-1) b* is postponed till after the
next class.