MATH 120 – Optimization

Fall 2007

Professor: Dr. Janet Vassilev
Office: Surge 233

Office Hours:  M 10-11 am, W 12-1 pm, F 9-10 am and by appointment.
Telephone: (951) 827-3020
email: jvassil@ucr.edu

webpage: http://math.ucr.edu/~jvassil

Text : An Introduction to Optimization, 2^rd Edition, by Chong and Zak

Overview: Optimization is the process of finding the maximum or minimum value of a function. In both Calculus 9A and Multivariable Calculus 10A, you have already had a brief introduction to optimizing one variable and multivariable functions. The tools at hand were first and second derivatives. In this course we will review the skills you learned in multivariable calculus using the language of linear algebra. Then we will forge ahead and learn about linear programming and the simplex method for maximizing linear functions on polyhedra. Knowing and being comfortable with linear algebra is a must in this course.

Course Meetings:  The course lectures will be held in Sproul Hall 2340 on Mondays, Wednesdays and Fridays at 11:10 am-12 pm. Discussion sessions will be held on Thursday (7:10 am) with Jenn Burke (003) or (7:40 am) with Tiff Troutman (002). You are expected to attend both the lectures and the discussion sessions as per Math Department decree.

Tips for Success: * Come to class! It is amazing how much you can learn by being attentive in class.  * Collaborative learning is encouraged but remember only YOU will be taking the quizzes and exams... * Like all mathematics, Optimization is not a spectator sport; you will learn only by doing!  You will find that a consistent effort will be rewarded. * Be organized.   Have a notebook or binder for Linear Algebra alone to keep your class notes, homework, quizzes and exams in order.  * No question you have should be left unanswered.  Ask your questions in class, discussion session or take advantage of office hours.

Homework (100 points):  Homework will be assigned every Wednesday and will be collected during the next week’s discussion session. No late homework will be accepted. Homework will not be graded unless it is written in order and labeled appropriately. An answer alone will get 0 points. Make sure to justify every answer. Your lowest homework score will be dropped and the remaining homework will be averaged to get a score out of 100.

Quizzes (100 points):  At least once every week there will be a short quiz given at the beginning of each lecture testing you on the definitions and theory that you learned from last class. You may use your notes. Quizzes will only last 5 minutes so make sure that your notes are organized and that you arrive on time for class. There may also be a quiz at the end of discussion with one problem similar to the homework problems assigned during the previous week. You may not use your notes for this quiz. The in class quizzes will be worth 3 points each, the lowest three will be dropped and the remaining will be averaged to obtain a score out of 50 points. The discussion quizzes will be worth 10 points each, there will be at least 6, and I will keep only the top 5 scores for a total of 50 points.

Exams (300 points):  I will give one midterm (100 points) and a final (200 points). Please bring your ID to each exam. There are no make up exams. If a test is missed, notify me as soon as possible on the day of the exam. For the midterms only, if you have a legitimate and documented excuse, your grade will be recalculated without that test. The Midterm is tentatively scheduled on Friday, October 26. The Final is on Wednesday, December 13, from 8-11 am.

Grades:  General guidelines for letter grades (subject to change; but they won't get any more strict): 90-100% - A; 80-89% - B; 70-79% - C; 60-69% - D; below 60% - F.  In assigning Final Grades for the course, I will compare your grade on all course work (including the Final) and your grade on the Final Exam. You will receive the better of the two grades.

Calculator Policy:  It is the Math Department’s policy to forbid the use of calculators on both exams and quizzes.

Tentative Schedule (for Dr. Vassilev’s Optimization):

Date	Sections	Topic	Homework/Notes
9/28	3.1-3.2	Introduction/Linear Algebra Review
10/1	3.3	Linear Algebra Review Continued
10/3	3.4	Quadratic Forms	HW1
10/5	3.5	Matrix Norms
10/8	4.1-4.2	Linear Varieties and Segments
10/10	4.3-4.5/5.2	Convex Sets/The Derivative	HW2
10/12	5.3-5.4	Computing the Derivative
10/15	5.5,5.6,6.1	Level Sets, Taylor Series
10/17	6.2,19.1-19.3	Tests for Local Extrema, Tangent Space	HW3
10/19	19.4	Lagrange Multipliers
10/22	19.5-19.6	Second Order Conditions for Lagrange
10/24		Review (Review Sheet)	HW4-HW5
10/26		Midterm
10/29	20.1	Karush-Kuhn-Tucker Condition
10/31	20.1	Karush-Kuhn-Tucker Condition
11/2	15.1-15.4	Intro to Linear Programming
11/5	15.5-15.6	Reducing to standard form and Basic Solutions
11/7	15.7-15.8	Properties of Basic Solutions/Geometry and Linear Programming	HW6
11/9	16.1	Row Operations
11/14	16.2	Canonical Augmented Matrix	HW7
11/16		Midterm 2
11/19	16.3	Updating the Canonical Matrix
11/21	16.4	The Simplex Algorithm
11/26	16.5	Matrix form of the Simplex Method
11/28	16.6	Two-phase Simplex Method	HW8
11/30	16.7	Revised Simplex Method
12/3	17.1	Dual Linear Programs
12/5	17.2	Properties of Dual Problems
12/7		Review	Final Review Sheet
12/13		Final