346:002, Fall 2019

An Introduction to Optimization Theory

General Course Information
Meeting time:  Monday and Wednesday 11:30 am - 12:45 pm in W303 W201

: Hao Huang

Textbook: P. Thie and G. Keough, An Introduction to Linear Programming and Game Theory, 3/e

Please click here for the syllabus of this course, which includes more details on the course goal, grading scheme, exam and homework policy.

My Contact Information
E-mail: hao.huang AT emory.edu
Office: MSC E432
Office hour: Monday/Wednesday 10:30am-11:30am or by appointment.

Communicating with me:  If you have a general question about this class, you are welcome to send me an email. For mathematical questions, the best way is to come to my office hour, or talk to me after class. If you cannot make it to these, you can send me an email to make an appointment with me. Please include the course number in the subject line of your emails.

Homework Assigments
The homework assignements will be posted below, together with their due dates.

2.2.8, 2.2.12, 2.3.7, 2.3.16, 2.3.23        (due date: Sep 11, 2019).       Solution to HW1

HW2: 2.4.4, 2.4.6, 2.5.3, 2.6.9, 3.1.3 (e) and (f), 3.9.6      (due date: Sep 18, 2019).

HW3: (I) 3.2.2, (II) 3.2.6, (III) solve the LP in Exercise 3.3.2 on Page 76 using the general representation theorem (a.k.a. fundamental theorem of LP), (IV) prove
that the intersection of a finite number of convex sets is still convex.      (due date: Sep 25, 2019) 

Tentative Outline
Chapter 1: Mathematical Models (2-3 classes)
Chapter 2: The Linear Programming Model (1-2 classes)
Chapter 3: The Simplex Method (7 classes)
Chapter 4: Duality (4-5 classes)
Chapter 5: Sensitivity Analysis (2-3 classes)
Chapter 6: Integer Programming (2 classes)
Chapter 7: The Transportation Problem (2-3 classes)
Chapter 9:  Two-Person, Zero-Sum Games (2-3 classes)

Course Schedule 

The materials covered in the classes will be updated and posted below after each class.

Aug 28 (W)      
Course introduction, how to formulate a problem in mathematical languages, diet problem, introduction and assumptions of general linear programming (Ch 1.1, 1.2, 2.1)

Sep 2 (M)        ---- Labor day, no class          

Sep 4 (W)         Blending model, the graphical method to solve 2-variable LP, Portfolio problem (Ch 2.2).         

Sep 9 (M)
        Production Model, transportation model, convert a LP into standard form. (Ch 2.3, 2.4, 3.1)        

Sep 11 (W)        Canonical form of LE/LP, basic feasible solutions (BFS) of LP, definition of convex sets (Ch 3.1, 3.2, 3.9)

Sep 16 (M)     
  Definition of extreme points, a proof that Extreme points of feasible region of LP in standard form = BFS. Definition of directions

Sep 18 (W)
         Definition of unit and extreme directions. Solve a LP using the Generation Representation Theorem.

Sep 23 (M)

Sep 25 (W)        

Sep 30 (M)

Oct 2 (W)        

Oct 7 (M) 

Oct 9 (W)        
----  Midterm 1  

Oct 14 (M)
         ---- Fall break, no class!

Oct 16 (W)     

Oct 21 (M)

Oct 23 (W)    

Oct 28 (M)    

Oct 30 (W)

Nov 4 (M)    

Nov 6 (W)    

Nov 11 (M)

Nov 13 (W)
         ----  Midterm 2

Nov 18 (M)       

Nov 20 (W)     

Nov 25 (M)     

Nov 27 (W)
         ---- Thanksgiving break, no class!     
Dec 2 (M)  

Dec 4 (W)     

Dec 9 (M)  

Dec 17 (Tu)           The final exam will be on Dec 17, 2019, Tuesday from 3:00pm to 5:30pm in the usual classroom (MSC W201)!