On the properties of interval linear programs with a fixed coefficient matrix

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10365255" target="_blank" >RIV/00216208:11320/17:10365255 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-319-67308-0_40" target="_blank" >http://dx.doi.org/10.1007/978-3-319-67308-0_40</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-319-67308-0_40" target="_blank" >10.1007/978-3-319-67308-0_40</a>

Result language
angličtina
Original language name
On the properties of interval linear programs with a fixed coefficient matrix
Original language description
Interval programming is a modern tool for dealing with uncertainty in practical optimization problems. In this paper, we consider a special class of interval linear programs with interval coefficients occurring only in the objective function and the right-hand-side vector, i.e. programs with a fixed (real) coefficient matrix. The main focus of the paper is on the complexity-theoretic properties of interval linear programs. We study the problems of testing weak and strong feasibility, unboundedness and optimality of an interval linear program with a fixed coefficient matrix. While some of these hard decision problems become solvable in polynomial time, many remain (co-)NP-hard even in this special case. Namely, we prove that testing strong feasibility, unboundedness and optimality remains co-NP-hard for programs described by equations with non-negative variables, while all of the weak properties are easy to decide. For inequality-constrained programs, the (co-)NP-hardness results hold for the problems of testing weak unboundedness and strong optimality. However, if we also require all variables of the inequality-constrained program to be non-negative, all of the discussed problems are easy to decide.
Czech name
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Czech description
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Project
<a href="/en/project/GA13-10660S" target="_blank" >GA13-10660S: Interval methods for optimization problems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Optimization and Decision Science: Methodologies and Applications: ODS, Sorrento, Italy, September 4-7, 2017
ISBN
978-3-319-67308-0
ISSN
2194-1017
e-ISSN
neuvedeno
Number of pages
9
Pages from-to
393-401
Publisher name
Springer
Place of publication
Cham
Event location
Sorrento, Italy
Event date
Sep 4, 2017
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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