## matthias beck

some of matt's pictures

MATH 430

Mathematics of Optimization

Fall 2018

 Lecture Mon/Wed/Fri 9:00-9:50 a.m. TH 211 Prerequisites: MATH 325 with a grade of C or better Instructor Dr. Matthias Beck Office Thornton Hall 933 Office hours Mon 11-12, Wed 10-11, Fri 1-2 & by appointment

Course objectives. Mathematics of Optimization introduces linear optimization models, their solution techniques, and interpretation of these solutions. Specifically, students will be able to

• model an optimization problem as a linear program and solve it using the simplex method;
• interpret the solution of the simplex algorithm in order to perform sensitivitiy analysis;
• model discrete optimization problems as integer programs and solve them using cutting-plane and branch-and-bound methods.

Student Learning Outcomes. A skeleton of what you are expected to know & do at the end of the course is as follows:

• Linear programming models: modeling optimization problems as linear programs
• Geometry of linear programs: understanding the geometry of linear inequalities
• Simplex algorithm: using the simplex algorithm to solve linear programs
• Sensitivity analysis: executing sensitivity analysis of objective function coefficients and constraint right-hand sides
• Dual linear programs: constructing the dual linear program
• Duality theorems: articulating the consequences of the strong duality and complementary slackness theorems
• Integer programming methods: formulating various combinatorial optimization problems as integer linear programs
• Solving integer programs: performing Gomory's cutting-plane and branch-and-bound methods

Textbook. Dimitris Bertsimas & John N. Tsitisklis, Introduction to Linear Optimization, Athena Scientific, 1997.

The math. The way to learn math is through doing math. It is vital and expected that you attend every lecture. You will get a good feel for the math from there, but it is even more crucial that you do the homework. Working in groups is not only allowed but strongly recommended. While I strongly encourage you to work together, the solutions and writing projects you hand in have to be your own. I will assign weekly homework, each will be due the following Tuesday.

 Homework 40% Midterm Exam (22-24 October) 30% Final Exam (19 December, 8:00-10:15am) 30%

I want to ensure that each of you accomplishes the goals of this course as comfortably and successfully as possible. At any time you feel overwhelmed or lost, please come and talk with me.

Fine print.