**UT Arlington Faculty:** Bill Corley, Jay Rosenberger

**Collaborators:** Wei-Chang Yeh

**Ph.D. Students:** T. K. Sung (2006), Goh Saito (2012), Alireza Noroziroshan (2016)

**Funding:** Texas Advanced Technology Program 2004-06

**Topics:** Linear programming

**Description:** The standard linear programming
model is an indispensable tool in today’s manufacturing environment, and
scientific and business computing expends significant effort toward
solving linear programming problems and its variants. Moreover, such
applications demand the solution of increasingly large problems in
nearly real time. In response, the Constraint Optimal Selection
Technique (COST) approach for large-scale linear programming problems
appears significantly more efficient other methods. Its basic idea is to
consider only those constraints that are likely to determine an optimal
basic feasible solution by associating a measure of this likelihood
with each constraint. Various metrics have been and are being developed.
Current research is also directed at extending COSTs to solve mixed
integer programming problems. This extension may ultimately provide a
nearly real-time solution to any degree of accuracy for any optimization
problem or system of mathematical relations utililizing the “discretize
then optimize” approach. Toward this end, a patent has been filed for
the COST method.

- Saito, G., H. W. Corley, J. M. Rosenberger, and T.-K. Sung (2012). “Constraint Optimal Selection Techniques (COSTs) for Nonnegative Linear Programming Problems.” COSMOS Technical Report 04-02. The University of Texas at Arlington. Arlington, TX.
- Yeh, Wei-Chang, H.W. Corley (2009) “A Simple Direct Cosine Simplex Algorithm.”
*Applied Mathematics and Computation*,**214**, 178-186. - Corley, H.W., Rosenberger, T.-K. Sung, and W.-C. Yeh (2006). “The Cosine Simplex Algorithm.”
*International Journal of Advanced Manufacturing Technology*,**27**, 1047-1050. - Rosenberger, J. M., T.-K. Sung, and H. W. Corley (2004). “A Geometric Active-Set Extension of the Simplex Method.” COSMOS Technical Report 04-07.