Interval convex quadratic programming problems in a general form

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10365246" target="_blank" >RIV/00216208:11320/17:10365246 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s10100-016-0445-8" target="_blank" >http://dx.doi.org/10.1007/s10100-016-0445-8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10100-016-0445-8" target="_blank" >10.1007/s10100-016-0445-8</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Interval convex quadratic programming problems in a general form

Popis výsledku v původním jazyce

This paper addresses the problem of computing the minimal and the maximal optimal value of a convex quadratic programming (CQP) problem when the coefficients are subject to perturbations in given intervals. Contrary to the previous results concerning on some special forms of CQP only, we present a unified method to deal with interval CQP problems. The problem can be formulated by using equation, inequalities or both, and by using sign-restricted variables or sign-unrestricted variables or both. We propose simple formulas for calculating the minimal and maximal optimal values. Due to NP-hardness of the problem, the formulas are exponential with respect to some characteristics. On the other hand, there are large sub-classes of problems that are polynomially solvable. For the general intractable case we propose an approximation algorithm. We illustrate our approach by a geometric problem of determining the distance of uncertain polytopes. Eventually, we extend our results to quadratically constrained CQP, and state some open problems.

Název v anglickém jazyce

Interval convex quadratic programming problems in a general form

Popis výsledku anglicky

This paper addresses the problem of computing the minimal and the maximal optimal value of a convex quadratic programming (CQP) problem when the coefficients are subject to perturbations in given intervals. Contrary to the previous results concerning on some special forms of CQP only, we present a unified method to deal with interval CQP problems. The problem can be formulated by using equation, inequalities or both, and by using sign-restricted variables or sign-unrestricted variables or both. We propose simple formulas for calculating the minimal and maximal optimal values. Due to NP-hardness of the problem, the formulas are exponential with respect to some characteristics. On the other hand, there are large sub-classes of problems that are polynomially solvable. For the general intractable case we propose an approximation algorithm. We illustrate our approach by a geometric problem of determining the distance of uncertain polytopes. Eventually, we extend our results to quadratically constrained CQP, and state some open problems.

Druh

J_imp - Článek v periodiku v databázi Web of Science

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 periodika

Central European Journal of Operations Research

ISSN

1435-246X

e-ISSN

—

Svazek periodika

25

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

13

Strana od-do

725-737

Kód UT WoS článku

000407369000012

EID výsledku v databázi Scopus

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