This is the homepage for Math 170, Mathematical Methods for Optimization, in the Spring of 2007. General information about the course can be found here . A syllabus can be found here . This document is where weekly updates and homework assignments can be found. Homeworks are due the following week during class on Wednesdays.

New updates on the syllabus were done on Feb. 23.

• Solution to Hwk 5 is now available here in postscript and here in pdf .
• Solution to Hwk 6 is now available here in postscript and here in pdf .
• We will start our semester project very soon, using matlab. For introduction to matlab, see An Online Matlab Primer.
• Here is the term project, in pdf and in ps formats.

Matlab Codes

• Here is a Matlab session to solve an LP. Download it, and try to run something similar to get familiar with the Simplex Method.
• Here is an interactive Matlab program to solve an LP with a shorted Simplex Tableau. Download it along with functions SimplexTableau.m and getr.m to run the simplex method.
• Here is another interactive Matlab program to solve an LP with Extended Simplex Tableau. Download it along with functions SimplexTableau.m and getr.m to run the simplex method based on updating the Simplex Tableau.
• Here is the third interactive Matlab program to solve an LP with the Revised Simplex Tableau. Download it along with functions SimplexTableau.m and getr.m to run the simplex method. You should compare three versions in both the results (they should be almost identical) and the computations involving the Tableaus.
• Here is an interactive Matlab program to solve two-person zero-sum game using the Revised Simplex Tableau. Download it along with functions RevisedSimplex.m and getr.m to give it a try.
• Here is an ILP solver using the revised simplex tableau. Download it along with function ILPRevisedSimplex.m . Give it a try.

Here is a NetworkFlow solver based on the idea of unsaturated path. The solver is based on the algorithm in the book and hence is not very efficient, but it does get the job done for small to middle sized networks. Try it with a driver routine .

Here is a Optimal Assignment code based on Network Flows.

Here is a code for solving the Transportation Problem based on Network Flow code above.

Here is a code for solving the Quadratic Programming Problem based on Wolfe's Algorithm. You need the subroutines QPRevisedSimplex.m and Revisedgetr.m for the code to work.

Here is a sample LP solver using the revised simplex tableau for the canonical LP problem. Download it along with functions ILPRevisedSimplex.m , RevisedSimplexTableau.m , and Revisedgetr.m . You can base your project on these codes if you so choose.

Here are two unfinished codes BLPRevisedSimplex.m for doing the simplex method on the bounded LP and BURevisedgetr.m for changing the index when a variable from the upper bound has been pushed downward to reduce the objective. Again the codes are incomplete. You can choose to write your own code based on them.