Math 6050                         Optimization                      Spring 2017

 

Instructor: Professor Jim Zhu
Office: 5516 EV, Tel: 387-4535, e-mail: zhu@wmich.edu
Web: http://homepages.wmich.edu/~zhu/
Office Hours: T. R. 9:50-10:40am and 1:50-2:40pm. Office:  EV5516
Class Hours:  T.R..12:30-1:45pm Rood Hall 03307
Text:  Techinques of Variational Analysis, by J. M. Borwein and Q.J. Zhu, Springer, New York, N. Y. 2005.
Reference: Convex Analysis and Nonlinear Optimization, Springer, New York, N. Y. 2000.


Course Description:

This is a topic course covering selected optimization methods and their applications. Topics are decided by the instructors and may change from year to year. This year we will focus on Variational Techniques and its applications. After discuss the basic method we turn to applications in diverse areas.  Topics include inequalities, matrix theory, nonsmooth analysis, approximation theory, economics and finance. This course often attracts students from different disciplines. Students are encouraged to participate in class discussions and to contribute ideas from their disciplines.

Prerequisites:

MATH 272 and 408 or 608 or IEGM 610 or other courses approved by the instructor.

Objectives:

We will start from Lagrange multiplier rule for constrained optimization problems. We will take a variational approach and emphasize the economic explanation for the Lagrange multipliers and then related the Lagrange multiplier to duality theory.

Next we turn to applications in financial models. Since maximize concave utility and minimize convex risk is often the primary concern these financial problems are often convex. Making the convex duality theory particularly suitable tools.  It is often worthy noting the financial meaning of the Larange multipliers in these applications.

We will start with the simple model of portafolio theory in a finite economy and discuss various issues of importance to the financial community. We then generalize to trading theory that involves a multi-period economy.

Finally, we explore continuous financial models.

Academic Integrity: Students are responsible for making themselve aware of and understanding the policies and procedures in the Undergraduate (pp. 274-276) [Graduate (pp.25-27)] Catalog that pertain to Academic Honesty. These policies include cheating, fabrication, falsification and forgery, multiple submission, plagiarism, complicity and computer misuse. If there is reason to believe you have been involved in academic dishonesty, you will be referred to the Office of Student Conduct. You will be given the opportunity to review the charge(s). If you believe you are not responsible, you will have the opportunity for a hearing. You should consult with me if you are uncertain about an issue of academic honesty prior to the submission of an assignment or test.


Grading:

 Homework 55%, midterm 10%, class participations 10%, and the final 25%. The final exam will be 2:45-4:45pm on Wednesday, April 26.

Grading scale is approximately as follows:     

 A (85-100%) BA(78-84.99%) B (71-77.99%) CB(60-70.99%) and C below 60%.



 

 

Math 6050 Tentative Schedule  
Spring, 2017
Section Date Exercises/Due
1.1-2
 1/10
 1.3.1, 1.3.3-1.3.6/Jan 17
 2.1
1/12
 2.1.2/Jan 17
 2.3
 1/17,19
 2.3.1-2.3.4/Jan 24
 2.4
 1/24,26
2.4.2,2.4.3,2.4.6,2.4.7/Jan 31
 4.1
 1/31
4.1.1,4.1.6/Feb 7.
 4.2
 1/31
4.2.3,4.2.8/Feb. 7
 4.3
 2/2
4.3.1,4.3.4/Feb.14
 4.4
 2/7
4.4.3/Feb. 16
 
 2/9
midterm exam
 
 2/14
Review
 4.4
 2/16
4.4.6, 4.4.7/Feb. 21
 4.7
 2/21,23
4.7.2,4.7.3,4.7.5,4.7.10/Feb.28
 3.1
 2/28,3/2
3.1.4,3.1.5,3.1.6,3.1.8,3.1.12/Mar.14
 3.2
 3/14,16
3.2.1,3.2.2,3.2.5,3.2.6/Mar. 21
 3.3
3/21,23, 28
3.3.1,3.3.3/Mar. 30
 3.4
 3/30,4/4
3.4.13.4.4,3.4.7/April 6
 3.6
 4/6,11,13
3.6.1,3.6.3,3.6.7,3.6.9/April 18
 
4/18,20 Review
 Final
 4/26
2:45-4:45pm