# Argonne-National-Laboratory / DSP

An open-source parallel optimization solver for stochastic mixed-integer programming
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# DSP

DSP is an open-source and parallel package that implements decomposition methods for structured mixed-integer programming problems. These are structured optimization problems in the following form:

    minimize   c^T x + \sum_{s=1}^S q_s^T y_s
subject to   A x                              = b
T_s x +                    W_s y_s = h_s for s = 1, .., S
some x, y_s are integers


where x and y_s are decision variable vectors with dimensions n_1 and n_2, respectively, A, T_s and W_s are matrices of dimensions m_1 by n_1, m_2 by n_1 and m_2 by n_2, respectively, and c, q_s, b, and h_s are vectors of appropriate dimensions.

DSP Solution Methods:

• Extensive form solver (global solver)
• Serial/parallel dual decomposition (dual bounding solver)
• Serial/parallel Dantzig-Wolfe decomposition (global solver)
• Serial/parallel Benders decomposition

Problem Input Formats:

• SMPS file format for stochastic programs
• MPS and DEC files for generic block-structured optimization problems
• Julia modeling package Dsp.jl

## Documentation

The package documentation is available in Readthedocs.

## Credits

DSP has been developed and is maintained by:

• Kibaek Kim, Mathematics and Computer Science Division, Argonne National Laboratory.
• Victor M. Zavala, Department of Chemical and Biological Engineering, University of Wisconsin-Madison.

## Acknowledgements

This material is based upon work supported by the U.S. Department of Energy, Office of Science, under contract number DE-AC02-06CH11357. We gratefully acknowledge the computing resources provided on Blues, a high-performance computing cluster operated by the Laboratory Computing Resource Center at Argonne National Laboratory. We thank E. Michael Gertz and Stephen Wright for providing the OOQP software package.

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