9:00 am - 10:00 am: Simplex algorithms for linear programming.
Simplex algorithms are the classic methods for solving linear programming problems. What simplex algorithms are now available, what are their computational properties, and which should be used in a particular application? Included will be a discussion of primal and dual steepest-edge algorithms. New parallel simplex algorithms will also be briefly mentioned.
10:00 am - 10:15 am: Break.
10:15 am - 11:15 am: Barrier algorithms for linear programming
The primal-dual predictor-corrector barrier algorithm for linear programming has been shown to be the most computationally effective among the various algorithms that are related to logarithmic barrier functions. For which problems are these algorithms indicated? What can be done to improve their performance? New parallel barrier algorithms will also be described.
11:15 am - 11:30 am: Break.
11:30 am - 12:00 pm: Integer programming algorithms
Like essentially all other commerical integer-programming codes, the CPLEX mixed-integer (MIP) optimizer is built around branch-and-bound. In addition, it uses problem preprocessing, cutting-plane generation and various node selection and branching rules. Among the branching rules is a new rule known as "strong branching," which is particularly effective for problems with weaker LP-relaxations. Finally, the CPLEX MIP algorithms now run in parallel on SGI multi-processors.
12:30 pm - 2:00 pm: Lunch.
2:00 pm - 3:00 pm: The CPLEX callable library.
The CPLEX callable library contains many features that allow the efficient solution of large-scale models. An overview of the callable library will be given, with a discussion of the CPLEX object-oriented data model and a summary of the various features that are available to model developers and algorithm designers.
3:00 pm - 3:15 pm: Break
3:15 pm - 4:15 pm: Combining a model, data and the callable library.
Often, modeling systems such as AIMMS, AMPL, GAMS, or MPL are used to prototype a model for a particular application. In order to gain the best performance from the optimizer, it is necessary to translate the model into a representation involving a computer programming language. An example of this process will be illustrated, with the emphasis on maintaining the separation between model and data, as well as how to effectively use the CPLEX callable library to obtain results for an application.
4:15 pm - 4:30 pm: Break
4:30 pm - 5:30 pm: Building new algorithms using the CPLEX callable library.
For large scale problems, it is often not efficient to simply apply one of the CPLEX solvers directly to the problem. Specialized algorithmic approaches may be necessary. A specific real-world example will be described, and it will be illustrated how the CPLEX callable library can be used to build a fast algorithm for solving this problem.