The polyhedral projection problem

Benjamin Weißing ()
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Benjamin Weißing: Friedrich-Schiller-University

Mathematical Methods of Operations Research, 2020, vol. 91, issue 1, No 4, 55-72

Abstract: Abstract We revisit the polyhedral projection problem. This problem has many applications, among them certain problems in global optimisation, polyhedral calculus, problems encountered in information theory and financial mathematics. In particular, it has been shown recently that polyhedral projection problems are equivalent to vector linear programmes (which contain multiple objective linear programmes as a sub-class). In this article, we develop a novel solution concept which provides more detailed insights into the structure of the projected polyhedron by taking its lineality space into account. We explore the relationship of our new solution concept to a previous one. We extend the problem class of vector linear programmes by using pre-orders instead of partial orders. We then show that solutions (according to the lattice approach) to such vector linear programmes can be derived by solving a related polyhedral projection problem.

Keywords: Vector optimization; Set optimization; Computational geometry (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00186-019-00677-7

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