SBmethod --- A C++ Implementation of the Spectral Bundle Method. Manual to Version 1.1
Please always quote using this URN: urn:nbn:de:0297-zib-6039
- \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.
Author: | Christoph Helmberg |
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Document Type: | ZIB-Report |
Tag: | eigenvalue optimization; large-scale problems; semidefinite programming; semidefinite relaxations; spectral bundle method |
MSC-Classification: | 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90-04 Explicit machine computation and programs (not the theory of computation or programming) |
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C06 Large-scale problems | |
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C22 Semidefinite programming | |
Date of first Publication: | 2000/10/10 |
Series (Serial Number): | ZIB-Report (00-35) |
ZIB-Reportnumber: | 00-35 |