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  2. Simplex algorithm - Wikipedia

    en.wikipedia.org/wiki/Simplex_algorithm

    In each simplex iteration, the only data required are the first row of the tableau, the (pivotal) column of the tableau corresponding to the entering variable and the right-hand-side. The latter can be updated using the pivotal column and the first row of the tableau can be updated using the (pivotal) row corresponding to the leaving variable.

  3. Bland's rule - Wikipedia

    en.wikipedia.org/wiki/Bland's_rule

    In mathematical optimization, Bland's rule (also known as Bland's algorithm, Bland's anti-cycling rule or Bland's pivot rule) is an algorithmic refinement of the simplex method for linear optimization. With Bland's rule, the simplex algorithm solves feasible linear optimization problems without cycling. [1] [2] [3]

  4. Revised simplex method - Wikipedia

    en.wikipedia.org/wiki/Revised_simplex_method

    The revised simplex method is mathematically equivalent to the standard simplex method but differs in implementation. Instead of maintaining a tableau which explicitly represents the constraints adjusted to a set of basic variables, it maintains a representation of a basis of the matrix representing the constraints. The matrix-oriented approach ...

  5. Pivot element - Wikipedia

    en.wikipedia.org/wiki/Pivot_element

    The pivot or pivot element is the element of a matrix, or an array, which is selected first by an algorithm (e.g. Gaussian elimination, simplex algorithm, etc.), to do certain calculations. In the case of matrix algorithms, a pivot entry is usually required to be at least distinct from zero, and often distant from it; in this case finding this ...

  6. Method of analytic tableaux - Wikipedia

    en.wikipedia.org/wiki/Method_of_analytic_tableaux

    A graphical representation of a partially built propositional tableau. In proof theory, the semantic tableau [1] (/ t æ ˈ b l oʊ, ˈ t æ b l oʊ /; plural: tableaux), also called an analytic tableau, [2] truth tree, [1] or simply tree, [2] is a decision procedure for sentential and related logics, and a proof procedure for formulae of first-order logic. [1]

  7. 'He shouldn't have done that': Donald Trump criticizes ... - AOL

    www.aol.com/news/shouldnt-done-donald-trump...

    Donald Trump said in an interview with Fox News that Ukrainian President Volodymyr Zelenskyy "shouldn't have allowed" war in his country to happen.

  8. Dual linear program - Wikipedia

    en.wikipedia.org/wiki/Dual_linear_program

    The proof establishes that, once the simplex algorithm finishes with a solution to the primal LP, it is possible to read from the final tableau, a solution to the dual LP. So, by running the simplex algorithm, we obtain solutions to both the primal and the dual simultaneously. [1]: 87–89 Another proof uses the Farkas lemma. [1]: 94

  9. Accused rapist found not guilty because he has ‘sexsomnia ...

    www.aol.com/news/accused-rapist-found-not-guilty...

    An Australian man has been found not guilty of rape after blaming it on “sexsomnia.” Timothy Malcolm Rowland, 40, was found not guilty of rape after a seven-day trial after jurors agreed that ...