-
Sufficient matrices : properties, generating and testingNagy, Marianna E.- ...This paper investigates various aspects of sufficient matrices, one of the most relevant matrix classes introduced in connection with linear complementarity problems. We summarize the most important ... theoretical results and properties related to sufficient matrices. Based on these, we propose different construction rules that can be used to generate new matrices that belong to this class. A nonnegative number can be assigned to each sufficient matrix, which is called its handicap and works as a measure of sufficiency. The handicap plays a crucial role in proving convergence and complexity results for interior point algorithms for linear complementarity problems. For a particular sufficient matrix, called Csizmadia’s matrix, we give the exact value of the handicap, which is exponential in the size of the matrix. Another important topic that we address is deciding whether a matrix is sufficient. Tseng proved in 2000 that this decision problem is co-NP hard. We investigate three different algorithms for determining the sufficiency of a given matrix: Väliaho’s algorithm, a linear programming-based algorithm, and an algorithm that facilitates nonlinear programming reformulations of the definition of sufficiency. We tested the efficiency of these methods on our recently launched benchmark data set that consists of four different sets of matrices. In this paper, we give the description and most important properties of the benchmark set, which can be used in the future to compare the performance of different interior point algorithms for linear complementarity problems.Source: Journal of optimization theory and applications. - ISSN 0022-3239 (Aug. 2023, str. 1-33)Type of material - article, component part ; adult, seriousPublish date - 2023Language - englishCOBISS.SI-ID - 183125251
Author
Nagy, Marianna E.- |
Illés, Tibor |
Povh, Janez, 1973- |
Varga, Anita |
Žerovnik, Janez, 1958-
Topics
linear algebra |
optimization theory |
sufficient matrices |
P∗(κ)-matrices |
linear complementarity problem |
linearna algebra |
teorija optimizacije |
zadostne matrike |
P∗(κ)-matrike |
problem linearne komplementarnosti
Shelf entry
Permalink
- URL:
Impact factor
Access to the JCR database is permitted only to users from Slovenia. Your current IP address is not on the list of IP addresses with access permission, and authentication with the relevant AAI accout is required.
Year | Impact factor | Edition | Category | Classification | ||||
---|---|---|---|---|---|---|---|---|
JCR | SNIP | JCR | SNIP | JCR | SNIP | JCR | SNIP |
Select the library membership card:
DRS, in which the journal is indexed
Database name | Field | Year |
---|
Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
---|---|
Nagy, Marianna E.- | |
Illés, Tibor | |
Povh, Janez, 1973- | 22649 |
Varga, Anita | |
Žerovnik, Janez, 1958- | 03430 |
Select pickup location:
Material pickup by post
Notification
Subject headings in COBISS General List of Subject Headings
Select pickup location
Pickup location | Material status | Reservation |
---|
Please wait a moment.