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A note on generalised linear complementarity problems
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| Zeitschriftentitel: | Bulletin of the Australian Mathematical Society |
|---|---|
| Personen und Körperschaften: | , |
| In: | Bulletin of the Australian Mathematical Society, 18, 1978, 2, S. 161-168 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
Cambridge University Press (CUP)
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| Schlagwörter: |
| author_facet |
Parida, J. Sahoo, B. Parida, J. Sahoo, B. |
|---|---|
| author |
Parida, J. Sahoo, B. |
| spellingShingle |
Parida, J. Sahoo, B. Bulletin of the Australian Mathematical Society A note on generalised linear complementarity problems General Mathematics |
| author_sort |
parida, j. |
| spelling |
Parida, J. Sahoo, B. 0004-9727 1755-1633 Cambridge University Press (CUP) General Mathematics http://dx.doi.org/10.1017/s000497270000798x <jats:p>Given an<jats:italic>n</jats:italic>×<jats:italic>n</jats:italic>matrix<jats:italic>A</jats:italic>, an<jats:italic>n</jats:italic>-dimensional vector<jats:italic>q</jats:italic>, and a closed, convex cone<jats:italic>S</jats:italic>of<jats:italic>R<jats:sup>n</jats:sup></jats:italic>, the generalized linear complementarity problem considered here is the following: find a<jats:italic>z</jats:italic>∈<jats:italic>R<jats:sup>n</jats:sup></jats:italic>such that</jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" mimetype="image" position="float" xlink:type="simple" xlink:href="S000497270000798X_eqnU1" /></jats:disp-formula></jats:p><jats:p>where<jats:italic>s</jats:italic>* is the polar cone of<jats:italic>S</jats:italic>. The existence of a solution to this problem for arbitrary vector<jats:italic>q</jats:italic>has been established both analytically and constructively for several classes of matrices<jats:italic>A</jats:italic>. In this note, a new class of matrices, denoted by<jats:italic>J</jats:italic>, is introduced.<jats:italic>A</jats:italic>is a<jats:italic>J</jats:italic>-matrix if</jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" mimetype="image" position="float" xlink:type="simple" xlink:href="S000497270000798X_eqnU2" /></jats:disp-formula></jats:p><jats:p>The new class can be seen to be broader than previously studied classes. We analytically show that for any<jats:italic>A</jats:italic>in this class, a solution to the above problem exists for arbitrary vector<jats:italic>q</jats:italic>. This is achieved by using a result on variational inequalities.</jats:p> A note on generalised linear complementarity problems Bulletin of the Australian Mathematical Society |
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Cambridge University Press (CUP), 1978 |
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Cambridge University Press (CUP), 1978 |
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0004-9727 1755-1633 |
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0004-9727 1755-1633 |
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English |
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1978 |
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Cambridge University Press (CUP) |
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ai |
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Bulletin of the Australian Mathematical Society |
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49 |
| title |
A note on generalised linear complementarity problems |
| title_unstemmed |
A note on generalised linear complementarity problems |
| title_full |
A note on generalised linear complementarity problems |
| title_fullStr |
A note on generalised linear complementarity problems |
| title_full_unstemmed |
A note on generalised linear complementarity problems |
| title_short |
A note on generalised linear complementarity problems |
| title_sort |
a note on generalised linear complementarity problems |
| topic |
General Mathematics |
| url |
http://dx.doi.org/10.1017/s000497270000798x |
| publishDate |
1978 |
| physical |
161-168 |
| description |
<jats:p>Given an<jats:italic>n</jats:italic>×<jats:italic>n</jats:italic>matrix<jats:italic>A</jats:italic>, an<jats:italic>n</jats:italic>-dimensional vector<jats:italic>q</jats:italic>, and a closed, convex cone<jats:italic>S</jats:italic>of<jats:italic>R<jats:sup>n</jats:sup></jats:italic>, the generalized linear complementarity problem considered here is the following: find a<jats:italic>z</jats:italic>∈<jats:italic>R<jats:sup>n</jats:sup></jats:italic>such that</jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" mimetype="image" position="float" xlink:type="simple" xlink:href="S000497270000798X_eqnU1" /></jats:disp-formula></jats:p><jats:p>where<jats:italic>s</jats:italic>* is the polar cone of<jats:italic>S</jats:italic>. The existence of a solution to this problem for arbitrary vector<jats:italic>q</jats:italic>has been established both analytically and constructively for several classes of matrices<jats:italic>A</jats:italic>. In this note, a new class of matrices, denoted by<jats:italic>J</jats:italic>, is introduced.<jats:italic>A</jats:italic>is a<jats:italic>J</jats:italic>-matrix if</jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" mimetype="image" position="float" xlink:type="simple" xlink:href="S000497270000798X_eqnU2" /></jats:disp-formula></jats:p><jats:p>The new class can be seen to be broader than previously studied classes. We analytically show that for any<jats:italic>A</jats:italic>in this class, a solution to the above problem exists for arbitrary vector<jats:italic>q</jats:italic>. This is achieved by using a result on variational inequalities.</jats:p> |
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url_ver=Z39.88-2004&ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fvufind.svn.sourceforge.net%3Agenerator&rft.title=A+note+on+generalised+linear+complementarity+problems&rft.date=1978-04-01&genre=article&issn=1755-1633&volume=18&issue=2&spage=161&epage=168&pages=161-168&jtitle=Bulletin+of+the+Australian+Mathematical+Society&atitle=A+note+on+generalised+linear+complementarity+problems&aulast=Sahoo&aufirst=B.&rft_id=info%3Adoi%2F10.1017%2Fs000497270000798x&rft.language%5B0%5D=eng |
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| author | Parida, J., Sahoo, B. |
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| author_sort | parida, j. |
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| description | <jats:p>Given an<jats:italic>n</jats:italic>×<jats:italic>n</jats:italic>matrix<jats:italic>A</jats:italic>, an<jats:italic>n</jats:italic>-dimensional vector<jats:italic>q</jats:italic>, and a closed, convex cone<jats:italic>S</jats:italic>of<jats:italic>R<jats:sup>n</jats:sup></jats:italic>, the generalized linear complementarity problem considered here is the following: find a<jats:italic>z</jats:italic>∈<jats:italic>R<jats:sup>n</jats:sup></jats:italic>such that</jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" mimetype="image" position="float" xlink:type="simple" xlink:href="S000497270000798X_eqnU1" /></jats:disp-formula></jats:p><jats:p>where<jats:italic>s</jats:italic>* is the polar cone of<jats:italic>S</jats:italic>. The existence of a solution to this problem for arbitrary vector<jats:italic>q</jats:italic>has been established both analytically and constructively for several classes of matrices<jats:italic>A</jats:italic>. In this note, a new class of matrices, denoted by<jats:italic>J</jats:italic>, is introduced.<jats:italic>A</jats:italic>is a<jats:italic>J</jats:italic>-matrix if</jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" mimetype="image" position="float" xlink:type="simple" xlink:href="S000497270000798X_eqnU2" /></jats:disp-formula></jats:p><jats:p>The new class can be seen to be broader than previously studied classes. We analytically show that for any<jats:italic>A</jats:italic>in this class, a solution to the above problem exists for arbitrary vector<jats:italic>q</jats:italic>. This is achieved by using a result on variational inequalities.</jats:p> |
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| imprint | Cambridge University Press (CUP), 1978 |
| imprint_str_mv | Cambridge University Press (CUP), 1978 |
| institution | DE-D275, DE-Bn3, DE-Brt1, DE-Zwi2, DE-D161, DE-Gla1, DE-Zi4, DE-15, DE-Rs1, DE-Pl11, DE-105, DE-14, DE-Ch1, DE-L229 |
| issn | 0004-9727, 1755-1633 |
| issn_str_mv | 0004-9727, 1755-1633 |
| language | English |
| last_indexed | 2024-03-01T14:16:08.649Z |
| match_str | parida1978anoteongeneralisedlinearcomplementarityproblems |
| mega_collection | Cambridge University Press (CUP) (CrossRef) |
| physical | 161-168 |
| publishDate | 1978 |
| publishDateSort | 1978 |
| publisher | Cambridge University Press (CUP) |
| record_format | ai |
| recordtype | ai |
| series | Bulletin of the Australian Mathematical Society |
| source_id | 49 |
| spelling | Parida, J. Sahoo, B. 0004-9727 1755-1633 Cambridge University Press (CUP) General Mathematics http://dx.doi.org/10.1017/s000497270000798x <jats:p>Given an<jats:italic>n</jats:italic>×<jats:italic>n</jats:italic>matrix<jats:italic>A</jats:italic>, an<jats:italic>n</jats:italic>-dimensional vector<jats:italic>q</jats:italic>, and a closed, convex cone<jats:italic>S</jats:italic>of<jats:italic>R<jats:sup>n</jats:sup></jats:italic>, the generalized linear complementarity problem considered here is the following: find a<jats:italic>z</jats:italic>∈<jats:italic>R<jats:sup>n</jats:sup></jats:italic>such that</jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" mimetype="image" position="float" xlink:type="simple" xlink:href="S000497270000798X_eqnU1" /></jats:disp-formula></jats:p><jats:p>where<jats:italic>s</jats:italic>* is the polar cone of<jats:italic>S</jats:italic>. The existence of a solution to this problem for arbitrary vector<jats:italic>q</jats:italic>has been established both analytically and constructively for several classes of matrices<jats:italic>A</jats:italic>. In this note, a new class of matrices, denoted by<jats:italic>J</jats:italic>, is introduced.<jats:italic>A</jats:italic>is a<jats:italic>J</jats:italic>-matrix if</jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" mimetype="image" position="float" xlink:type="simple" xlink:href="S000497270000798X_eqnU2" /></jats:disp-formula></jats:p><jats:p>The new class can be seen to be broader than previously studied classes. We analytically show that for any<jats:italic>A</jats:italic>in this class, a solution to the above problem exists for arbitrary vector<jats:italic>q</jats:italic>. This is achieved by using a result on variational inequalities.</jats:p> A note on generalised linear complementarity problems Bulletin of the Australian Mathematical Society |
| spellingShingle | Parida, J., Sahoo, B., Bulletin of the Australian Mathematical Society, A note on generalised linear complementarity problems, General Mathematics |
| title | A note on generalised linear complementarity problems |
| title_full | A note on generalised linear complementarity problems |
| title_fullStr | A note on generalised linear complementarity problems |
| title_full_unstemmed | A note on generalised linear complementarity problems |
| title_short | A note on generalised linear complementarity problems |
| title_sort | a note on generalised linear complementarity problems |
| title_unstemmed | A note on generalised linear complementarity problems |
| topic | General Mathematics |
| url | http://dx.doi.org/10.1017/s000497270000798x |