References
- Broyden, C. G. (1998). A simple algebraic proof of Farkas’s lemma and related theorems. Optimization Methods and Software, 8(3–4), 185–5. https://doi.org/10.1080/10556789808805676
- Ciarlet, P. G. (1989). Introduction to numerical linear algebra and optimization. Cambridge University Press.
- Dax, A. (1993). The relationship between theorems of the alternative, least norm problems, steepest descent directions, and degeneracy: A review. Annals of Operations Research, 46(1), 11–60 https://doi.org/10.1007/BF02096256
- Dax, A., & Sreedharan, P. (1997). Theorems of the alternative and duality. Journal of Optimization Theory and Applications, 94(3), 561–590. https://doi.org/10.1023/A:1022644832111
- Galán, M. R. (2017). A theorem of the alternative with an arbitrary number of inequalities and quadraticprogramming. Journal of Global Optimization, 69(2), 427–442. https://doi.org/10.1007/s10898-017-0525-x
- Gale, D. (1960). The theory of linear economic models. McGraw-Hill.
- Giannessi, F. (1984). Theorems of the alternative and optimality conditions. Journal of Optimization Theory and Applications, 42(3), 331–365. https://doi.org/10.1007/BF00935321
- Gill, P. E., Murry, W., & Wright, M. H. (1991). Numerical linear algebra and optimization. Vol. 1 Addison-Wesley.
- Gordan, P. (1873). Über die auflösung linearer gleichungen mit reelen coefficienten. Mathematische Annalen, 6(1), 23–28. https://doi.org/10.1007/BF01442864
- Horn, R. A., & Johnson, C. R. (1990). Matrix analysis. Cambridge University Press.
- Kjeldsen, T. H. (2002). Different motivations and goals in the historical development of the theory of systems of linear inequalities. Archive for History of Exact Sciences, 56(6), 469–538. https://doi.org/10.1007/s004070200057
- Mangasarian, O. L. (1981). A stable theorem of the alternative: An extension of the Gordan theorem. Linear Algebra and Its Applications, 41, 209–223. https://doi.org/10.1016/0024-3795(81)90100-2
- Mccormick, G. P. (1983). Nonlinear programming. John Wiley.
- Osborne, M. R. (1985). Finite algorithms in optimization and data analysis. John Wiley & Sons.
- Saunders, B. D., & Schneider, H. (1979). Applications of the Gordan-Stiemke theorem in combinatorial matrix theory. SIAM Review, 21(4), 528–541. https://doi.org/10.1137/1021094
- Stiemke, E. (1915). Über positive Lösungen homogener linearer Gleichungen. Mathematische Annalen, 76(2–3), 340–342. https://doi.org/10.1007/BF01458147
- Tucker, A. W. (1956). Dual systems of homogeneous linear relations. In H. W. Kuhn & A. W. Tucker (Eds.), Linear Inequalities and Related Systems (pp. 3–18). Ann Math Stud. Princeton Univ. Press.
- Vajda, S. Mathematical programming, Addison Wesley: 1961.
- Wilkinson, J. H., & Reinsch, C. (1971). Linear algebra, handbook for automatic computation (Vol. 2). Springer-Verlag.