SYLLABUS FOR MATH 4420/5420

OPTIMIZATION


Professor Robert Carlson
Office: Engr 288
Phone: 255-3561

Class meets Tuesday-Thursday 10:50-12:05 in Osborne B213
Office hours: Official hours for this class are Tuesday-Thursday 9:30-10:30.
I am usually in my office M-F from 9:30 to 4:00. Exceptions are M-F 12-1 and TR 1:40-2:55.
You are welcome to stop by AT ANY TIME.
If you are making a special trip to campus to see me I suggest calling ahead.

NEWS:



The FINAL EXAM is on Tuesday 5/14 from 10:20-12:20.

Test 2 solutions

Linear programming notes
Linear programming problems with solutions

Homework 8, due Thursday 4/25
Text chapter 2, # 2, 3, 10, 12, 21

Homework 8 solutions

Homework 7

Homework 7 solutions

Notes on convexity

Notes on the Jacobi method



Homework 6
Homework 6 solutions

Some numerical methods notes

Test 1 solutions

Some linear algebra notes

Class notes - part 1

SOLUTIONS AT BOTTOM OF PAGE


COURSE DESCRIPTION:


In both pure and applied mathematics one often encounters optimization problems:
how does one maximize profit, minimize the fuel expended on a space mission to Mars,
or minimize the cost of visiting a collection of cities if the costs of travel
between pairs of cities is given?
This course will consider a collection of basic optimization problems and their solutions.
The emphasis is on `continuous' optimization,and the solution techniques use a lot of calculus,
linear algebra and geometry. The main topics are:
i) techniques from calculus (especially multivariate calculus),
ii) convex sets and functions,
iii) computer algorithms,
iv) linear programming,
v) least squares problems.
Additional topics may be covered if time permits.

TEXT

Peressini, Sullivan and Uhl, The Mathematics of Nonlinear Programming

Prerequisites:


Calculus III (Math 2350), Introduction to Linear Algebra (Math 3130)
Course calendar

Legal fine print:

The administration of the course described below is subject to change as deemed necessary by the instructor.

COMMENTS ON COLLABORATION

Students are encouraged to discuss homework problems with their classmates or with the professor to share ideas, or detect and correct errors.
However the written material handed in by the student is expected to be the work of that student.
Copying homework solutions, or partial solutions, from another student or source is a serious violation of the university's cheating policy.

DROP DATES AND OTHER POLICIES

The last day to drop is 4/5/19. Other policies and information from the Mathematics Department can be found at the Math home page. There is a "policies and information" link.

Disability Services

Students with disabilities may be entitled to support from Disability Services,
including extra time for examinations,in Main Hall 104, phone 255-3354.
Students who may fall into this group should talk to Disability Services as soon as possible.
The Disability Certification Letter to the professor is to be submitted within the first two weeks of classes.


Grading

In this course I expect 2 midterm examinations and a comprehensive final.
In addition there will be graded homework.
For undergraduates enrolled in Math 4420 I will discard the lowest two homework scores.
All homeworks will be counted for graduate students enrolled in Math 5420.
I expect to provide solutions for the homework. They will also be posted on this web page.
I can also provide paper copies if someone needs them.

Relative weights for grading purposes:
Homework 15 %
Each midterm 25 %
Final 35 %

HOMEWORK ASSIGNMENTS and SOLUTIONS will be available here

Homework 5
Homework 5 is due Thursday 3/7
Homework 5 solutions

Homework 4 is due Thursday 2/28
Text page 33-34 # 12 abc, 13, 14, 16, 18
Homework 4 solutions

Homework 3 is due Tuesday 2/19
Text page 31 # 2, 3, 4, 6, 9, 10abc
Homework 3 partial solutions

Homework 2 solutions

Homework 1 solutions

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