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The blockwise coordinate descent method for integer programs
Citation key JaegerSchoebel2019
Author Jäger, Sven and Schöbel, Anita
Pages 357–381
Year 2019
ISSN 1432-5217
DOI 10.1007/s00186-019-00673-x
Journal Mathematical Methods of Operations Research
Volume 91
Month June
Abstract Blockwise coordinate descent methods have a long tradition in continuous optimization and are also frequently used in discrete optimization under various names. New interest in blockwise coordinate descent methods arises for improving sequential solutions for problems which consist of several planning stages. In this paper we systematically formulate and analyze the blockwise coordinate descent method for integer programming problems. We discuss convergence of the method and properties of the resulting solutions. We extend the notion of Pareto optimality for blockwise coordinate descent to the case that the blocks do not form a partition and compare Pareto optimal solutions to blockwise optimal and to global optimal solutions. Among others we derive a condition which ensures that the solution obtained by blockwise coordinate descent is weakly Pareto optimal and we confirm convergence of the blockwise coordinate descent to a global optimum in matroid polytopes. The results are interpreted in the context of multi-stage linear integer programming problems and illustrated for integrated planning in public transportation.
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