This interactive seminar will provide an introduction to the powerful
computing environment of MATLAB and demonstrate the tools needed for
conducting research in combinatorics and optimization using MATLAB.
The first 60 minutes will focus on some of the basics of MATLAB, from
entering matrices, solving linear systems, and calculating
eigenvalues, to using the graphical features of MATLAB for plotting
functions and even graphs.
The second 60 minutes will look at writing
your own MATLAB programs (M-files), using symbolic MATLAB, and solving
both discrete and continuous optimization problems using the MOSEK
optimization toolbox.
bring up MATLAB help page (click on Help and choose MATLAB Help)
Click on Demos and then: +MATLAB -> +Mathematics -> Basic Matrix Operations
Matrices and Arrays:
MATrix LABoratory
vectors are nx1 matrices
click on: Run in the Command Window; click on Next when ready
Try to enter your own vector y=[....
Try to enter your own matrix Y=[....
Try the help command: help poly or help conv or try doc conv
Solve a system of linear equations: x=A\b - demo with
roundoff error example.
Try the test example file Asolve.m.
(Or use runAs.m.)
Now try the sample file Aoneseps.m.
(Or use runeps.m.) Can you explain the large error?!
(ASSIGN 1)
Plots:
Click on Demos and then: +MATLAB -> +Mathematics -> Optimal Fit of a Non-linear Function
Try:
help gplot; help ezplot; help spy
Symbolic Toolbox:
Close off +MATLAB;
+Toolboxes -> +Symbolic Math -> Symbolic Matrix Computation
MOSEK: A Guided Tour; First check path to find out where
MOSEK is or use: which mosekopt; then, use e.g. command
addpath /usr/msri/mathsw/mosek/4/toolbox/examp -end
cqo1 (Conic Opt using mosekopt and problem structure)
qco1 (quadrically constrained Opt using mosekopt and problem structure)
milo1 (Mixed Integer Opt using mosekopt and problem structure;
The Quadratic Assignment Problem:
An Example of Combinatorial Optimization - case study - try solving up
to n=?!!
(ASSIGN 2)
(See also QAPLIB;
add comments on Lagrangian and SDP relaxation)