Math 171A: Introduction to Numerical Optimization/Linear Programming

Winter 2017

MWF 12:00-12:50pm, Center Hall 214

Problems in all areas of mathematics, applied science, engineering, economics, medicine and statistics can be posed as optimization problems. An optimization problem begins with a set of independent variables or parameters, and often includes conditions or restrictions that define acceptable values of the variables. Such restrictions are known as the constraints of the problem. The other essential component of an optimization problem is a single measure of ``goodness'', termed the objective function, which depends in some way on the variables. The solution of an optimization problem is a set of allowed values of the variables for which the objective function assumes its ``optimal'' value. In mathematical terms, this usually involves maximizing or minimizing. Math 171A is primarily concerned with linear programming, which involves the minimization of a linear function subject to linear constraints.

For historical reasons, the subject is often also known as mathematical programming. However, it must be emphasized that mathematical programming has no direct connection with computer programming.

Some homework assignments will require the use of the package Matlab, although no prior knowledge of Matlab is assumed. Matlab enables the student to concentrate on the fundamental ideas of linear programming without becoming distracted by the rigors of mental arithmetic. (``It is unworthy of excellent men to lose hours like slaves in the labour of calculation.'' --- Leibniz.)


The course grade will be based on the homework assignments, midterm examinations and final examination, according to the following guidelines:
Written HW: 19%
Midterm 1 (Wednesday, February 1): 18%
Midterm 2 (Wednesday, March 8): 18%
Final (Wednesday, March 22, 11:30--2:30p): 45%

Homework assignments must be left in the homework dropbox (labeled 171A) located in the basement of AP&M.
Each assignment must be dropped off by 7:00pm on the due date stated on the assignment.

Class guidelines:

Class notes and homeworks:

Instructor: Philip E. Gill
Instructor's office: AP&M 5872
Instructor's office hours: Wednesday and Friday 10:30-11:30am, 1:30-2:30pm, or by appointment

TA: Yesheng Huang (
TA's office: AP&M 5412
TA's office hours: Thursday 3:30-5:30pm AP&M 5412
Section A01: Monday 5:00-5:50pm, AP&M 7421
Section A02: Monday 6:00-6:50pm, AP&M 7421

TA: Chao Fan (
TA's office: AP&M 5412
TA's office hours: Thursday 1:00-3:00pm AP&M 5412
Section A03: Monday 7:00-7:50pm, AP&M 7421
Section A04: Monday 8:00-8:50pm, AP&M 7421