Professor:
Weldon A. Lodwick
Office:
Telephone: 556‑8462 (office - voice mail), 556‑8442 (secretary), 556-8550 (fax)
E-Mail: weldon.lodwick@cudenver.edu
Web Site: http//:www-math.cudenver.edu/~wlodwick
Text:
Office
Hours: Mondays
Tuesdays/Thursdays
Other times by arrangement I may change office hours depending on the
accessibility of the above times
Students with Disabilities: If you have a disability that requires accommodation in this course, please see me as soon as possible. I am happy to make appropriate accommodations, provided timely notice is received.
Cell Phones: Please turn off your cell phones prior to entering the classroom. This is especially important when coming in for exams.
The proposed outline is
the initial guess of the topics that will be fruitful to investigate.
1.
Introduction
(notes)
a.
Preliminaries
b.
Introductory
Examples and Computer Demonstrations
2.
General
Mathematic Modeling Issues (notes and chapters 1-2 of Williams)
3.
Software
a.
MATLAB
Optimization Toolbox
b.
Excel
LP/NLP
4.
Optimization
Modeling Issues (chapters 3-11 of Williams)
a.
Model
Formulation
b.
Validation
c.
Model
Understanding
d.
Redundancy
and Infeasibility
e.
Algorithms
f.
Modeling
Languages (GAMS, TOMLABS, AMPLE, MODLER)
g. Model Equivalence
5.
Interval
Analysis, INTLAB and Optimization (notes)
6.
Optimization
Model Types (well concentrate on LP/NLP)
a.
Static
(Williams)
i.
Linear
ii.
Nonlinear
iii.
Integer
iv.
Mixed
Integer
b.
Uncertainty
Optimization (notes)
i.
Stochastic
ii.
Possibilistic and Fuzzy
c.
Heuristic
(notes)
i.
Genetic
Algorithms
ii.
Simulated
Annealing
iii.
Tabu
Search
d.
Dynamic
(notes)
i.
Dynamic
Programming
ii.
Optimal
Control
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. We will endeavor to discover how we mathematically know within the structure of this course. If we have a mathematical problem, it is because we dont know its solution. If we knew the solution, we would not have a problem. Thus, when we solve the problem, how do we know the answer we obtain is the solution to our problem? Thus to know mathematically (mathematical epistemology) is a central component of my teaching approach. This means that I believe it is important to know how one obtains the solution to a mathematical problem. Thus, it is imperative that you demonstrate the process by which you arrive at a solution, that is, you are to demonstrate knowledge of mathematics by articulating how you obtained the correct solution.
I believe that I am responsible to open the way, to encourage, and to, perhaps, 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 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 and quizzes 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 appropriate methods associated with aspects of optimization modeling weve studied this semester to correctly solve associated problems. Secondly, given a problem in optimization modeling, you should be able to: (i) translate the description of the problem into a (correct) mathematical model, (ii) choose and apply the appropriate software method(s), (iii) obtain the correct solution(s), and (iv) (correctly) interpret and display results. Lastly, by the end of the semester you should be able to judge, for yourself, the veracity of statements made in the areas of our study.
I do give +/- unless your school does
not recognize +/- grades in which case I grade without +/-.
A = 94%-100%
B+ = 88%-90% C+ = 78% - 80% D+ = 68% - 70%
A = 94%-100%
B = 84%-87% C =
74% - 77% D = 64% - 67%
A- =
91%-93% B- = 81%-83% C- =
71% - 73% D- = 60% - 63%
F less than 60%
** Graduate students will have extended content, be expected to have a deeper understanding, and be held to higher standards.
Note:
If your school does not
recognize plus/minus, then an A is 93% to 100%, B is 83% to 92%, C is 73% to
82%, D is 60% to 72% and an F is less than 60%.
Note: Problem sets will be due one week after we finish the associated topics
Literature review and annotated bibliography February 25th
Project proposal February 25th
Project division of labor March 8th
Midterm March 17th
Project
Reports May 9th
Final Exam May 10th or May 12th
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. The statistics that I have read about correctness of professors in grading and recording grades state that there is a 6% error rate. Please make sure that I have correctly graded and recorded your points.
Advice on exam taking: Some exams may be longer (or more demanding or both) than what you are accustomed. Thus, it is wise (imperative) for you take exams as follows. Do all the problems you can do first. Don't waste too much time on making sure that you have done your arithmetic correctly since arithmetic mistakes are usually discounted at half a point per mistake unless your arithmetic mistake totally trivializes the problem in which case the deduction will be severe. That is, you should work on generating the most number of points per unit of time.
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
Missing Examinations: If you miss a test for acceptable reasons and we have met before the test and agreed that indeed this is the case you will be given a make-up exam. You are to take the final exam on the given date. If you have more than two final exams on date of our final, this will have to be resolved at least one week in advance of our final exam. There are cases where an exam is missed without your being able to notify me ahead of time. These will be exceptional cases and we can work these out as long as your reasons are legitimate.
Legitimate Excuses: Legitimate excuses for missing tests and
quizzes are for some situations that are beyond your control. You may be required to produce official,
signed documentation. If you are needed
in a wedding, for example, you must talk to me prior to the (blessed) event.
If you are legally arrested, then this is not a legitimate excuse. For matters that are within your control, the
general rule is that it is not excused.
However, talk to me prior to
the event.
You are to review at least five sources that are relevant to your
project. This material needs to be at
the level of an upper-level undergraduate or graduate-level. That is, upper-level textbooks,
mathematical/operations research journals or other relevant journals are what is expected. If you
are in doubt about the level, please see me.
Each reference should be written (one page max/min) containing:
1.
(4%)
Synopsis of the content,
2.
(2%)
Evaluation as to the relevance/importance of the content toward your project,
3.
(2%) How
you are going to use the material in your project.
INSTRUCTIONS
FOR PROJECTS
A project consists of:
1.
Proposal A formal
written proposal is to be submitted for my approval. A proposal must contain:
a.
Title
b.
An optimization problem
c.
The description of the problem and the
data
d.
The methods (software) you will be using
to solve the problem
e.
Tasks and subtasks associated with the
problem
2.
Division of labor Once a
project is approved, the tasks and subtasks you have
identified in your project are given associated due-date, written up and
submitted to me.
3.
Software Each project will likely have
associated software development. If the
project does not have a software component, this section will be modified
according to the project proposal. The
components of the software development are:
a.
Code - the actual computer implementation
of the project. Attention must be paid
to efficiency, readability and portability.
b.
User interface the way
information is passed to the software must be compelling to the client.
c.
Data and inputs
d.
Execution - the algorithm
as run must correctly perform what it was designed to do.
e.
Output - relevant, clear
display of solution (tables, graphs, images).
f.
Ease ease of use.
g. Documentation
an in-line and hardcopy of the documentation on how to use the software
needs to be written. Moreover, help
files must be part of the software.
4. Testing each project
must have a test data set and the optimization model must run on the test
data. Part of the test data is for
debugging and verifying that the algorithm is working correctly. Other data is gathered to solve the specific
project problem.
FINAL PROJECT REPORT: Each person will need to submit a
final report. This will be done in
MS-Word or Latex. The final report will
(subject to modifications we uncover) consist of:
1.
Introduction
2.
Project
a.
Theoretical foundations theory,
application, algorithms
b.
Software description
c.
Results solutions, limitations and
improvements
3.
Opportunities for further research
4.
Conclusions
5.
Bibliography
6.
Appendices
a.
Source code
b.
Test problems and data
c.
Documentation