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9.<b>Farkas lemma: Generalizations; Linear optimization: Theorems of the alternative; Linear programming; Motzkin transposition theorem; Theorems of the alternative and optimization; Tucker homogeneous systems of linear relations</b><b>Farkas lemma: Generalizations; Fourier–Motzkin elimination method; Fractional programming; Global optimization: Envelope representation; Gröbner bases for polynomial equations; Kuhn–Tucker optimality conditions; Lagrangian duality: Basics; Least-index anticycling rules; Linear optimization: Theorems of the alternative; Linear programming; Motzkin transposition theorem; Theorems of the alternative and optimization; Tucker homogeneous systems of linear relations</b>FARKAS LEMMA
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