Abstract
Although the theorems of the alternative have been well known for a long time, their relationship to linear least squares problems and steepest descent directions was revealed only recently. This relationship was used by the author to derive a new theorem of the alternative. The present research extends this theorem to theℓ p norm,p > 1.
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References
A. Dax, “The computation of descent directions at degenerate points,” Technical Report, Hydrological Service of Israel (Jerusalem, 1985).
A. Dax, “A note on optimality conditions for the Euclidean multifacility location problem,”Mathematical Programming 36 (1986) 72–80.
A. Dax, “The relationship between theorems of the alternative, least squares problems and steepest descent directions,” Technical Report, Hydrological Service of Israel (Jerusalem, 1988).
A. Dax, “Theℓ 1 solution of linear equations subject to linear constraints,”SIAM Journal on Scientific and Statistical Computing 10 (1989) 328–340.
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Dax, A. A new theorem of the alternative. Mathematical Programming 47, 297–299 (1990). https://doi.org/10.1007/BF01580864
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DOI: https://doi.org/10.1007/BF01580864