SYLLABUS ‑ MATH 5595: Computational  Methods in Nonlinear Programming

Fall Semester ‑ 2001

Last update: Monday, August 20, 2001

Professor: Weldon A. Lodwick

Office: CU-Denver Building, Room 622

Telephone: 556‑8462 (office - voice mail), 556‑8442 (secretary), 556-8440 (fax)

E-Mail: weldon.lodwick@cudenver.edu

Web Site: http://www-math.cudenver.edu/~wlodwick

Text:       Jorge Nocedal and Stephen J. Wright, Numerical Optimization, Springer, 1999.

Office Hours:                Tu/Th                2:30-3:45 PM          CU-Denver Bldg 622

W                9:30-10:30 AM                CU-Denver Bldg 622

                                                Other times by appointment

 

Below is the proposed outline.  The weeks listed are tentative and indicate my best estimate as to the pace of the class.

PROPOSED COURSE OUTLINE

Date        Section                                                                  Read before class

8/21         Conduct of course and introduction                         

8/23         Apps and types of opt problems                                Chapter 1

8/28                Fundamentals of unconstrained                      Chapter 2 through “Two strategies”

                optimization I, types of solutions, algorithms

8/30                Fundamentals of unconstrained                      The rest of chapter 2

                optimization II

9/4           Line search methods, global convergence                Sections 3.1, 3.2

9/6           Local convergence of line search mthds                Section 3.3

9/11         Step length selection methods                 Section 3.4

9/13         Trust regions/the Cauchy Point Algorithm                Section 4.1

9/18         Using nearly exact solutions to the subprb   Section 4.2

9/20                Conjugate gradient methods for lin eqns       Section 5.1

9/25                Conjugate gradient methods                 Section 5.2 (through Polak-Ribiere)

9/27         Practical Newton methods                                  Sections 6.1, 6.2

10/2         Hessian modifications                                        Section 6.3

10/4         Trust Region Newton methods                 Section 6.4

10/9         Quasi-Newton methods (BFGS)                   Sections 8.1, 8.3

10/11                Introduction to constrained optimization                Section 12.1

10/16       First order conditions                                   Sections 12.2, 12.3

10/18       Second order conditions                                   Section 12.4

10/19       Take-home midterm due (5pm)

10/23                Fundamentals of algorithms for                       Sections 15.1, 15.2

                nonlinearly constrained optimization

10/25       Merit functions                                                               Section 15.3

10/30                Quadratic programming                                      Sections 16.1, 16.2

11/1                Inequality constraints, active set methods Sections 16.3, 16.4

11/6         Gradient projection                                              Section 16.6

11/8         Duality                                                                   Section 16.8

11/13                Quadratic penalty method                                 Section 17.1

11/15       Log barrier method                                      Section 17.2

11/20                Augmented Lagrangian method                   Sections 17.3, 17.4

11/27       SQP methods                                                 Sections 17.5, 18.1

11/29       Linear programming – simplex method                Sections 13.1, 13.2, 13.3

12/4         Interior point methods                                      Sections 14.1

12/6         Work on project

12/14       Final take-home due

 

MY APPROACH TO TEACHING

I believe that teaching is a process that involves an active partnership.  My role is that of a guide to your learning.  Therefore, I am responsible to open the way, to encourage, and to nudge you toward your own learning.  I will help guide you toward this learning by providing mathematics for you to experience.  It is my aim to communicate mathematics in a way that is supportive and nurturing of your efforts. Your role is to find a way to experience and articulate the mathematics that is presented and that you encounter.  I believe that it is your responsibility to let me know when you find yourself not understanding mathematical concepts that are presented in class.  Once you make this known, it is our responsibility to work on trying to attain clarity.  I will try to be as proactive as possible.  I believe that results on examinations, take-home quizzes, and projects give us the opportunity to clearly see where the areas of mathematical understanding are and what areas need more attention.

 

OUTCOMES

By the end of the semester you should be able to read, understand and apply numerical methods  for optimization associated with the topics covered in the semester to correctly solve associated problems at the level of our textbook.  Secondly, given a problem that requires optimization methods, you should be able to: (i) translate the description of the problem into an algorithm, (ii) choose and apply the appropriate software method(s), and (iii) obtain the correct solution(s).  Lastly, by the end of the semester, you should be able to judge for yourself, the veracity of statements made in optimization texts that are at the same level as our text. 

 

     EVALUATION

There are four evaluative criteria: (i) modeling and computer projects (30%, 300 points, of your grade), (ii) text-problems (20%, 200 points, of your grade), (iii) exams: midterm (22.5%, 225 points, of your grade) and final (22.5%, 225 points, of your grade) and (iv) in-class participation (5%, 50 points).  Evaluation is based on a point system so that it is very important that you turn in your projects and complete tests/quizzes as thoroughly as possible rather than taking a zero score.

 

IMPORTANT DATES:

Take-home midterm                  5 PM October 19th

Take-home final                                    5 PM December 14th

Others

 

The following distribution of grades is guaranteed.  However, the final distribution could be "curved" downward.

 

              A+ 97‑100%, A 93‑96.9%, A‑ 90‑92.9%

              B+ 87‑89.9%, B 83‑86.9%, B‑ 80‑82.9%

              C+ 77‑79.9%, C 73‑76.9%, C‑ 70‑72.9%

              D+ 67‑69.9%, D 63‑66.9%, D‑ 60‑62.9%

 

 

General advice: Keep all materials that I turn back in case you think I have not credited you with the points you earned.  I can only correct your score if you have what I have turned back to you. It is a good idea to xerox anything that you turn in just in case I lose what you turn in.  Please check to make sure that the points you earned are the points I have recorded.  Note: The statistics that I have read about correctness of professors in recording grades state that there is a 6% error rate in our recording of your grades.  Please make sure that I have correctly recorded your points.

 

POLICIES

Drops and incomplete grades: See Schedule of Courses for the relevant dates with respect to dropping this course.  The incomplete policy of the Mathematics Department and the College of Liberal Arts and Sciences is strictly enforced.  Incomplete grades are given only in situations in which a student who has been in good standing all semester, is prevented from completing a course assignment (for example the final exam) due to circumstances beyond her/his control (for example, hospitalization, jury duty, revised job assignments, death in the family).

 

Late Projects, Assignments: A penalty of 20% of the total points associated with the project or assignment per class period that a project or assignment is late will be assessed.  Take-home exams must be turned in on the due-date specified in this syllabus.

 

ASSIGNED PROBLEMS

Each problem is worth the same unless otherwise specified.  There will be K problems assigned over the course of the semester whose total will be 300 points; that is, each is worth 300/K points.  You can earn up to 200 points.  Another way of looking at it is that out of every 3 problems assigned, you need to correctly complete 2 to obtain a perfect score of 200 points.

 

You are welcome to fax or email me the assigned problem.  If you do fax assignments, please put on your cover sheet: Attention Professor Weldon A. Lodwick, number the pages, and make sure your name appears on each page.  If you email, please send your assignment as an attached file (in MS-Word, postscript, pdf, or latex format).

 

Date due                                Chapter/problem

9/7                           2/1, 3, 4, 7, 8, 9, 10, 11, 12, 13, 14

9/21                         3/2, 4, 5, 6, 8, 10

9/28                         4/1, 5, 6, 7, 9, 10

 

MODELING AND COMPUTER PROJECTS

You will be assigned problems to solve on the computer using GAMS, MATLAB, and your own algorithms using MATLAB or C++ for example.  The write-ups for the projects will be handed out within the next two weeks.

 

CLASS PARTICIPATION

You are expected to come to class prepared to discuss the material scheduled for that day.  This means that you need to read what is assigned before coming to class and be prepared to ask/answer questions about the material.  If what you read was not comprehensible, write down questions about the parts that you did not understand and bring these to class.  There are just a few of us.  Please, if you are unable to attend class, you need to let us know so that we can reschedule class. 

 

Your class participation points will be based on the following guidelines:

85% -100%: Active participation (and attendance) in class.  Meaningful questions, comments,

observations

70% - 85%: Usually prepared for class with occasional exceptions.  Able to answer the majority of

                                questions correctly, but may need some help

40% - 69%: Inconsistent participation, able to answer some questions

0% - 39%: Poor preparation, usually unprepared for class