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Volumn 19, Issue 1, 2008, Pages 234-239

A short algebraic proof of the Farkas lemma

Author keywords

Farkas lemma; Key theorem; Linearly ordered vector spaces; Motzkin's theorem; Systems of linear inequalities; Theorems of the alternative; Tucker's theorem

Indexed keywords

FARKAS LEMMA; KEY THEOREM; LINEARLY ORDERED VECTOR SPACES; MOTZKIN'S THEOREM; SYSTEMS OF LINEAR INEQUALITIES; THEOREMS OF THE ALTERNATIVE; TUCKER'S THEOREM;

EID: 61349160550     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/06067438     Document Type: Article
Times cited : (28)

References (22)
  • 2
    • 33947179411 scopus 로고    scopus 로고
    • Farkas' Lemma, other theorems of the alternative, and linear programming in infinite-dimensional spaces: A purely linear-algebraic approach
    • D. BARTL, Farkas' Lemma, other theorems of the alternative, and linear programming in infinite-dimensional spaces: A purely linear-algebraic approach, Linear Multilinear Algebra, 55 (2007), pp. 327-353.
    • (2007) Linear Multilinear Algebra , vol.55 , pp. 327-353
    • BARTL, D.1
  • 3
    • 0031649749 scopus 로고    scopus 로고
    • A simple algebraic proof of Farkas's lemma and related theorems
    • C. G. BROYDEN, A simple algebraic proof of Farkas's lemma and related theorems, Optim. Methods Softw., 8 (1998), pp. 185-199.
    • (1998) Optim. Methods Softw , vol.8 , pp. 185-199
    • BROYDEN, C.G.1
  • 5
    • 21344489679 scopus 로고
    • The relationship between theorems of the alternative, least norm problems, steepest descent directions, and degeneracy: A review
    • A. DAX, The relationship between theorems of the alternative, least norm problems, steepest descent directions, and degeneracy: A review, Ann. Oper. Res, 46 (1993), pp. 11-60.
    • (1993) Ann. Oper. Res , vol.46 , pp. 11-60
    • DAX, A.1
  • 6
    • 0031238059 scopus 로고    scopus 로고
    • An elementary proof of Farkas' lemma
    • A. DAX, An elementary proof of Farkas' lemma, SIAM Rev., 39 (1997), pp. 503-507.
    • (1997) SIAM Rev , vol.39 , pp. 503-507
    • DAX, A.1
  • 7
    • 33646697381 scopus 로고    scopus 로고
    • The distance between two convex sets
    • A. DAX, The distance between two convex sets, Linear Algebra Appl., 416 (2006), pp. 184-213.
    • (2006) Linear Algebra Appl , vol.416 , pp. 184-213
    • DAX, A.1
  • 9
    • 84941391018 scopus 로고
    • Theorie der einjachen Ungleichungen, 3.
    • J. FARKAS, Theorie der einjachen Ungleichungen, 3. Reine Angew. Math., 124 (1902), pp. 1-27.
    • (1902) Reine Angew. Math , vol.124 , pp. 1-27
    • FARKAS, J.1
  • 10
    • 0010143617 scopus 로고
    • On systems of linear inequalities
    • Systems, H. W. Kuhn and A. W. Tucker, eds, Annals of Mathematics Studies 38, Princeton University Press, Princeton, NJ
    • K. FAN, On systems of linear inequalities, in Linear Inequalities and Related Systems, H. W. Kuhn and A. W. Tucker, eds., Annals of Mathematics Studies 38, Princeton University Press, Princeton, NJ, 1956, pp. 99-156.
    • (1956) Linear Inequalities and Related , pp. 99-156
    • FAN, K.1
  • 12
    • 33947103496 scopus 로고
    • Systems of linear relations
    • R. A. GOOD, Systems of linear relations, SIAM Rev., 1 (1959), pp. 1-31.
    • (1959) SIAM Rev , vol.1 , pp. 1-31
    • GOOD, R.A.1
  • 14
    • 1842868854 scopus 로고
    • Über lineare Ungleichungen
    • Szeged
    • A. HAAR, Über lineare Ungleichungen, Acta Math. Szeged, 2 (1924), pp. 1-14.
    • (1924) Acta Math , vol.2 , pp. 1-14
    • HAAR, A.1
  • 15
    • 61349113949 scopus 로고    scopus 로고
    • A note on generalized Farkas alternatives
    • M. M. MARSH, A note on generalized Farkas alternatives, Topology Proc., 28 (2004), pp. 153-162.
    • (2004) Topology Proc , vol.28 , pp. 153-162
    • MARSH, M.M.1
  • 17
    • 61349180711 scopus 로고    scopus 로고
    • T. S. MOTZKIN, Contributions to the theory of linear inequalities, RAND Corporation Translation 22, RAND Corporation, Santa Monica, CA, 1952. Reprint in Theodore S. Motzkin: Selected Papers, D. Cantor, B. Gordon, and B. Rothschild, eds., Birkhäuser, Boston, 1983, pp. 1-80.
    • T. S. MOTZKIN, Contributions to the theory of linear inequalities, RAND Corporation Translation 22, RAND Corporation, Santa Monica, CA, 1952. Reprint in Theodore S. Motzkin: Selected Papers, D. Cantor, B. Gordon, and B. Rothschild, eds., Birkhäuser, Boston, 1983, pp. 1-80.
  • 19
    • 0033341726 scopus 로고    scopus 로고
    • Note on a paper of Broyden
    • C. ROOS AND T. TERLAKY, Note on a paper of Broyden, Oper. Res. Lett., 25 (1999), pp. 183-186.
    • (1999) Oper. Res. Lett , vol.25 , pp. 183-186
    • ROOS, C.1    TERLAKY, T.2
  • 21
    • 0001768599 scopus 로고
    • Dual systems of homogeneous linear relations
    • Systems, H. W. Kuhn and A. W. Tucker, eds, Annals of Mathematics Studies 38, Princeton University Press, Princeton, NJ
    • A. W. TUCKER, Dual systems of homogeneous linear relations, in Linear Inequalities and Related Systems, H. W. Kuhn and A. W. Tucker, eds., Annals of Mathematics Studies 38, Princeton University Press, Princeton, NJ, 1956, pp. 3-18.
    • (1956) Linear Inequalities and Related , pp. 3-18
    • TUCKER, A.W.1
  • 22
    • 3042994369 scopus 로고
    • A generalization of the Farkas lemma and applications to convex programming
    • C. ZǍLINESCU, A generalization of the Farkas lemma and applications to convex programming, J. Math. Anal. Appl., 66 (1978), pp. 651-678.
    • (1978) J. Math. Anal. Appl , vol.66 , pp. 651-678
    • ZǍLINESCU, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.