Checking weak optimality and strong boundedness in interval linear programming

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10397333" target="_blank" >RIV/00216208:11320/19:10397333 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=1VmXhFqDy-" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=1VmXhFqDy-</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00500-018-3520-3" target="_blank" >10.1007/s00500-018-3520-3</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Checking weak optimality and strong boundedness in interval linear programming

Popis výsledku v původním jazyce

Interval programming provides a mathematical tool for dealing with uncertainty in optimization problems. In this paper, we study two properties of interval linear programs: weak optimality and strong boundedness. The former property refers to the existence of a scenario possessing an optimal solution, or the problem of deciding non-emptiness of the optimal set. We investigate the problem from a complexity-theoretic point of view and prove that checking weak optimality is NP-hard for all types of programs, even if the variables are restricted to a single orthant. The property of strong boundedness implies that each feasible scenario of the program has a bounded objective function. It is co-NP-hard to decide for inequality-constrained interval linear programs. For this class of programs, we derive a sufficient and necessary condition for testing strong boundedness using the orthant decomposition method. We also discuss the open problem of checking strong boundedness of programs described by equations with nonnegative variables.

Název v anglickém jazyce

Checking weak optimality and strong boundedness in interval linear programming

Popis výsledku anglicky

Interval programming provides a mathematical tool for dealing with uncertainty in optimization problems. In this paper, we study two properties of interval linear programs: weak optimality and strong boundedness. The former property refers to the existence of a scenario possessing an optimal solution, or the problem of deciding non-emptiness of the optimal set. We investigate the problem from a complexity-theoretic point of view and prove that checking weak optimality is NP-hard for all types of programs, even if the variables are restricted to a single orthant. The property of strong boundedness implies that each feasible scenario of the program has a bounded objective function. It is co-NP-hard to decide for inequality-constrained interval linear programs. For this class of programs, we derive a sufficient and necessary condition for testing strong boundedness using the orthant decomposition method. We also discuss the open problem of checking strong boundedness of programs described by equations with nonnegative variables.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

50201 - Economic Theory

Projekt

<a href="/cs/project/GA18-04735S" target="_blank" >GA18-04735S: Nové přístupy pro relaxační a aproximační techniky v deterministické globální optimalizaci</a><br>

Návaznosti

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

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Soft Computing

ISSN

1432-7643

e-ISSN

—

Svazek periodika

23

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

9

Strana od-do

2937-2945

Kód UT WoS článku

000465459700009

EID výsledku v databázi Scopus

2-s2.0-85053505477