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The criss-cross algorithm works on a standard pivot tableau (or on-the-fly calculated parts of a tableau, if implemented like the revised simplex method). In a general step, if the tableau is primal or dual infeasible, it selects one of the infeasible rows / columns as the pivot row / column using an index selection rule.
"The linear complementarity problem, sufficient matrices, and the criss-cross method" (PDF). Linear Algebra and Its Applications. 187: 1–14. doi: 10.1016/0024-3795(93)90124-7. Murty, Katta G. (January 1972). "On the number of solutions to the complementarity problem and spanning properties of complementary cones" (PDF).
Another modification showed that the criss-cross algorithm, which does not maintain primal feasibility, also visits all the corners of a modified Klee–Minty cube. [7] Like the simplex algorithm, the criss-cross algorithm visits all 8 corners of the three-dimensional cube in the worst case.
Simplex pivot methods preserve primal (or dual) feasibility. On the other hand, criss-cross pivot methods do not preserve (primal or dual) feasibility – they may visit primal feasible, dual feasible or primal-and-dual infeasible bases in any order. Pivot methods of this type have been studied since the 1970s. [29]
In 1985 and 1987, Terlaky independently published on the criss-cross algorithm. [4] [5] [6] The theory of oriented matroids has also been used by Terlaky and Zhang (1991) to prove that their criss-cross algorithms have finite termination for linear programming problems.
My go-to method for years has been (for two of us): five large eggs, one large yolk, salt and pepper, and a splash of cream. I cook the whisked eggs in butter, over the lowest heat possible on the ...
Another basis-exchange pivoting algorithm is the criss-cross algorithm. [41] [42] There are polynomial-time algorithms for linear programming that use interior point methods: these include Khachiyan's ellipsoidal algorithm, Karmarkar's projective algorithm, and path-following algorithms. [15]
At around 600 miles wide and up to 6,000 meters (nearly four miles) deep, the Drake is objectively a vast body of water. To us, that is. To the planet as a whole, less so.