A Collection of Systems Arising from Interior-Point Methods for Quadratic Optimization
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README.md
assembleK2.m
assembleK3.m
assembleK35.m
cycle_through_problems.m
getK.m
read_blocks.m

README.md

Interior-Point Systems

DOI

This repository contains a collection of linear systems arising from interior-point methods for quadratic optimization in MatrixMarket format. The distinguishing features of the collection are that

  • systems contain accompanying right-hand sides
  • systems are supplied in the form of their blocks, allowing users to solve several equivalent formulations of the same systems
  • sets of related systems are supplied, generated during the iterations of an interior-point method applied to the same optimization problem

Usage

A Matlab interface to the systems is provided. From the top-level folder,

[P, K, nz, rhs] = getK(@my_assembler, problem, iter, @my_preconditioner, args...)

returns the system generated from problem problem at interior-point iteration iter in K and rhs. The assembler @my_assembler assembles the system from its blocks, as read by read_blocks(). Example assemblers are provided in assembleK3, assembleK35 and assembleK2. If supplied, my_preconditioner should return an adequate preconditioner P together with a measure of its "complexity" (e.g., its number of nonzeros) in nz. Additional arguments args... are passed unchanged to my_preconditioner. If no preconditioner is supplied, P is set to a sparse identity matrix.

See the technical report below for examples.

Citing this Collection

If you use this collection in your research, please cite the following sources

  1. Orban D., A Collection of Linear Systems Arising from Interior-Point Methods for Quadratic Optimization, Cahier du GERAD G-2015-00, GERAD, Montreal, Canada, 2015. BibTeX.
  2. Orban D., A Collection of Linear Systems Arising from Interior-Point Methods for Quadratic Optimization, online data set, 2015. BibTeX.