http://interval.louisiana.edu/courses/655/656-spring-2004-outline.html

Math. 656 Course Outline


As of December 6, 2003, this page is still under development.  Further details will be added soon.
This outline is a tentative guide, and will be updated as the course progresses.  Time will be allocated as appropriate for student presentations and discussion.

Refer to the course description for the topic and overall goals of this course.  Generally, the emphasis this semester is on implementation and application of the techniques we studied last semester.

Note: Some of the material referenced below may be copyrighted, and hence is not generally available by clicking on it. Please email me, rbk@louisiana.edu, and I will email you either a Postscript or a PDF copy of the appropriate excerpts, according to the ``fair use" provision of the copyright law.

Home page for the course
Bibliography for the course in PDF format
 

 
Topic no.  Description Explanation / References / Projects
1.
    Review of code lists (also known as "tapes" or "Directed Acyclic Graphs" or DAG's ) and GlobSol
 See the book Rigorous Global Search, Continuous Problems (Kearfott, Kluwer, 1996), and also see the GlobSol components overload/codlvars.f90 and overload/overload.f90 (module CODELIST_CREATION).  To generate code lists, use the scripts and programs fmake, makegrad, and optimize_codelist.  To exhibit code lists in a readable form, use prntcodl.  (See me about using GlobSol on the Sparc's and about possibly installing it, and the necessary compiler, on personal machines.)
2.
Implementation of finding the approximate LP solution and the Neumaier / Shcherbina / Jansson validation procedure
 See LP_interface/(run_find_LP_solution find_lp_solution Neumaier_validate_LP).f90 in GlobSol.  Also check out the routine DSPLP in the Slatec library.  (Look at /mathpkgs/SLATEC/dsplp.f on our Ultra system.)  Projects include:
  • thorough testing.  (What strategy should we use for testing?  What problems should we use to test?)
3.
Creation of an approximating  LP from a code list
 See create_LP_problem/(LP_operations test_LP_operations).f90 in GlobSol.  The basic structure and most basic linear operations are already implemented in module LP_OPERATIONS.  Projects include:
  • filling in other operations and standard functions that we have been analyzing;
  • thoroughly testing what we presently have.
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    Further discussion of applications: Minimax problems
    		 We should review what we have done and identify what we need to do.
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    Structural analysis problems 
    		 (tentative) A personal visit from George Corliss (week of March 8)
    6
    More extensive testing of the convex underestimator implementation
    		  The idea here is to go beyond the testing for correct programming (which presumably we have done), and to test the value of the implementation in solving actual problems.  Possible sources of test problems include
    7. Study of an alternate general environment: The COCONUT project The COCONUT project was a collaboration to develop and open-source, extensible environment for global optimization.  We can install this C++ environment, and we can contribute to it.  References may include:
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