Generation of interior points and polyhedral representations of cones in $${\mathbb {R}}^N$$ R N cut by $${\varvec{M}}$$ M planes sharing a common point

Alexander Belyaev ()

Mathematical Methods of Operations Research, 2016, vol. 83, issue 1, 85 pages

Abstract: The following paper describes a method for solving certain non-convex minimization problems. These problems contain properties where the feasible region may be represented as a union of convex cones. This set of cones is generated by the intersection of finitely many half-spaces passing through a defined origin. Globally the problem is non-convex, but it is locally convex within the interior of the generated cones whereas the objective function tends to infinity elsewhere. The following algorithm results in a polyhedral representation of all of the cones and an interior point in each of them. In order to solve the problem globally, a convex optimization algorithm is required to be initialized at each interior point and to converge to the local minimum over the corresponding cone. The best of these solutions is the global optimum. A study of the time complexity is presented herewith along with a detailed computational analysis. Copyright Springer-Verlag Berlin Heidelberg 2016

Keywords: Linear homogeneous systems; Algorithm; Projection method; Hyperplanes in $${\mathbb {R}}^N$$ R N; 52C45; 52C35 (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1007/s00186-015-0520-2 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:mathme:v:83:y:2016:i:1:p:71-85

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/00186

DOI: 10.1007/s00186-015-0520-2

Access Statistics for this article

Mathematical Methods of Operations Research is currently edited by Oliver Stein

More articles in Mathematical Methods of Operations Research from Springer, Gesellschaft für Operations Research (GOR), Nederlands Genootschap voor Besliskunde (NGB)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().