346:002, Fall 2019
An Introduction to Optimization Theory
Monday and Wednesday 11:30 am - 12:45 pm in W303 W201
Instructor: Hao Huang
Thie and G. Keough, An
Introduction to Linear Programming and Game Theory, 3/e
Syllabus: Please click here for the
syllabus of this course, which includes more details on the course
goal, grading scheme, exam and homework policy.
E-mail: hao.huang AT
Office: MSC E432
10:30am-11:30am or by appointment.
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
the course number in the subject line of your emails.
assignements will be posted below, together with their due dates.
2.2.12, 2.3.7, 2.3.16, 2.3.23
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,
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)
covered in the classes will be updated and posted below after each
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
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)
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)
exam will be on Dec 17,
2019, Tuesday from 3:00pm to 5:30pm in the usual classroom (MSC W201)!