PROPERTIES OF THE SOLUTION SET OF ABSOLUTE VALUE EQUATIONS AND THE RELATED MATRIX CLASSES

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10472178" target="_blank" >RIV/00216208:11320/23:10472178 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=0xwyWGHuIx" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=0xwyWGHuIx</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/22M1497018" target="_blank" >10.1137/22M1497018</a>

Jazyk výsledku

angličtina

Název v původním jazyce

PROPERTIES OF THE SOLUTION SET OF ABSOLUTE VALUE EQUATIONS AND THE RELATED MATRIX CLASSES

Popis výsledku v původním jazyce

The absolute value equations (AVE) problem is an algebraic problem of solving Ax+|x| = b. So far, most of the research has focused on methods for solving AVE, but we address the problem itself by analyzing properties of AVE and the corresponding solution set. In particular, we investigate topological properties of the solution set, such as convexity, boundedness, or connect-edness, or whether it consists of finitely many solutions. Further, we address problems related to the nonnegativity of solutions such as solvability or unique solvability. AVE can be formulated by means of different optimization problems, and in this regard we are interested in how the solutions of AVE are related with optima, Karush-Kuhn-Tucker points, and feasible solutions of these optimization problems. We characterize the matrix classes associated with the above mentioned properties and inspect the computational complexity of the recognition problem; some of the classes are polynomi-ally recognizable, but some others are proved to be NP-hard. For the intractable cases, we propose various sufficient conditions. We also post new challenging problems that were raised during the investigation of the problem.

Název v anglickém jazyce

PROPERTIES OF THE SOLUTION SET OF ABSOLUTE VALUE EQUATIONS AND THE RELATED MATRIX CLASSES

Popis výsledku anglicky

The absolute value equations (AVE) problem is an algebraic problem of solving Ax+|x| = b. So far, most of the research has focused on methods for solving AVE, but we address the problem itself by analyzing properties of AVE and the corresponding solution set. In particular, we investigate topological properties of the solution set, such as convexity, boundedness, or connect-edness, or whether it consists of finitely many solutions. Further, we address problems related to the nonnegativity of solutions such as solvability or unique solvability. AVE can be formulated by means of different optimization problems, and in this regard we are interested in how the solutions of AVE are related with optima, Karush-Kuhn-Tucker points, and feasible solutions of these optimization problems. We characterize the matrix classes associated with the above mentioned properties and inspect the computational complexity of the recognition problem; some of the classes are polynomi-ally recognizable, but some others are proved to be NP-hard. For the intractable cases, we propose various sufficient conditions. We also post new challenging problems that were raised during the investigation of the problem.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GA22-11117S" target="_blank" >GA22-11117S: Globální analýza citlivosti a stabilita v optimalizačních úlohách</a><br>

Návaznosti

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

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

SIAM Journal on Matrix Analysis and Applications

ISSN

0895-4798

e-ISSN

1095-7162

Svazek periodika

44

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

21

Strana od-do

175-195

Kód UT WoS článku

000974412700006

EID výsledku v databázi Scopus

2-s2.0-85151064442