90-04 Explicit machine computation and programs (not the theory of computation or programming)
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Modern applications of mathematical programming must take into account a multitude of technical details, business demands, and legal requirements. Teaching the mathematical modeling of such issues and their interrelations requires real-world examples that are well beyond the toy sizes that can be tackled with the student editions of most commercial software packages. We present a new tool, which is freely available for academic use including complete source code. It consists of an algebraic modeling language and a linear mixed integer programming solver. The performance and features of the tool are in the range of current state-of-the-art commercial tools, though not in all aspects as good as the best ones. Our tool does allow the execution and analysis of large real-world instances in the classroom and can therefore enhance the teaching of problem solving issues. Teaching experience has been gathered and practical usability was tested in classes at several universities and a two week intensive block course at TU Berlin. The feedback from students and teachers has been very positive.
Constraint Programs and Mixed Integer Programs are closely related optimization problems originating from different scientific areas. Today's state-of-the-art algorithms of both fields have several strategies in common, in particular the branch-and-bound process to recursively divide the problem into smaller sub problems. On the other hand, the main techniques to process each sub problem are different, and it was observed that they have complementary strenghts. We propose a programming framework {\sffamily SCIP} that integrates techniques from both fields in order to exploit the strenghts of both, Constraint Programming and Mixed Integer Programming. In contrast to other proposals of recent years to combine both fields, {\sffamily SCIP} does not focus on easy implementation and rapid prototyping, but is tailored towards expert users in need of full, in-depth control and high performance.
ZIMPL User Guide
(2001)
\texttt{SBmethod}, Version 1.1, is an implementation of the spectral bundle method for eigenvalue optimization problems of the form \begin{displaymath} \min_{y\in \mathbf{R}^m}\;\; a\;\lambda_{\max}(C-\sum_{i=1}^{m} A_i y_i)+b^Ty. \end{displaymath} The design variables $y_i$ may be sign constrained, $C$ and and $A_i$ are given real symmetric matrices, $b\in\mathbf{R}^m$ allows to specify a linear cost term, and $a>0$ is a constant multiplier for the maximum eigenvalue function $\lambda_{\max}(\cdot)$. The code is intended for large scale problems and allows to exploit structural properties of the matrices such as sparsity and low rank structure. The manual contains instructions for installation and use of the program. It describes in detail input format, options, and output. The meaning of the variables and parameters is made precise by relating them to a mathematical description of the algorithm in pseudocode.