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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

50201 - Economic Theory

Projekt

<a href="/cs/project/GA13-10660S" target="_blank" >GA13-10660S: Intervalové metody pro optimalizační úlohy</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

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

Počet stran výsledku

9

Strana od-do

393-401

Název nakladatele

Springer

Místo vydání

Cham

Místo konání akce

Sorrento, Italy

Datum konání akce

4. 9. 2017

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—