MATH 6025: Topics in Optimization - Optimization Under Uncertainty, Theory, Algorithms

 

Professor:   Weldon A. Lodwick

                   University of Colorado at Denver

                   Department of Mathematics - Campus Box 170

                   622 CU-Denver Building

Telephone: 303.556.8462 (office)

                   303.556.8442 (secretary)

Email:         wlodwick@math.cudenver.edu

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

Office Hours:    I’m in most days.  When my door is open, come in.  Otherwise, just make an appointment.  I will make specific times available to the class after we find out what times work best for the class.

 

The class will study the current state of the theory and algorithms in optimization under uncertainty.  The proposed topics to be covered by the class are:

1.      An introduction to stochastic optimization - theory and algorithms (4 weeks)

2.      An introduction to possibilistic and fuzzy optimization - theory and algorithms (6 weeks)

3.      An introduction to other optimization under uncertainty (2 weeks)

4.      An introduction to heuristics applied to continuous optimization under uncertainty problems (4 weeks)

a.       Genetic algorithms

b.      Simulated annealing

c.       Tabu search

d.      Hybrid heuristic methods

 

Texts

1. Liu, Baoding.  The Theory and Practice of Uncertainty Programming.  Physica-

    Verlag/Springer Verlag, 2002. (recommended text)

2. Ramik, Jaroslav and Vlach, Milan.  Generalized Concavity in Fuzzy Optimization and Decision

   Analysis.  Kluwer Publishers, 2002. (I have the library copy)

3. Kall, Peter and Wallace, Stein W.   Stochastic Optimization (you can download the text at

    http://www.unizh.ch/ior/Pages/Deutsch/Mitglieder/Kall/bib/ka-wal-94.pdf )

 

General Articles

1. Sahinidis, Nickolaos V., “Optimization under uncertainty: State-of-the-art and opportunities”

 (download from my web page under this class)

2. Sen, Surrajeet and Higle, Julia L. “An introductory tutorial on stochastic linear programming models,” Interfaces 29: March-April 1999, pp. 33-61.

 

Specific Articles and Notes

These will be given during the semester.

__________________________________________________________

Pre-requisite: Experience/familiarity at the graduate level optimization course such as Math 5594 or Math 5595.

 

EVALUATION - GRADING

 

I.                    Reading – report and in-class presentation of a two research articles (100 points each).  You can find an article that interests you and/or I can suggest article(s).  Either way, please make an appointment to get the articles approved.

II.                 Project – this can be an application, computer system that uses one or more of the methods we study, survey research study, or theoretical development.  In any case, please get approval from me by giving me a proposal and making an appointment to discuss your proposal.

III.               Assignments - four assignments (75 points each), due roughly once every three weeks.  These will be handed out and posted.

IV.              Take-home final

 

Research article                                                          200 points

Project                                                                         300 points

Assignment                                                                   250 points (50 points extra)

Final                                                                             250 points

                                                                                    ----

Total                                                                          1000 points

 

A     950 – 1000 points (the university does not recognize A+ as a grade)

A-    900 –  949 points

B+   870  – 899 points

B     840  – 869 points

B-    800 –  839 points

C     below 750  points