Abstract
Methods perform very differently when solving a same problem. It is common that a problem that is solved slowly by the simplex method would be solved fast by the dual simplex method; and vise versa. Consequently, LP packages often include multiple options to be chosen, as it seems to be impossible to predetermine which method would be better to solve a given problem. Pursuing a method with features of both the primal and dual methods, scholars have attempted to combine primal and dual simplex methods for years. A class of resulting variants may be described by “criss-cross” because of their switching between primal and dual iterations. The primal-dual algorithm (Sect. 7.1) and the self-dual parametric simplex algorithm (Sect. 7.2) may be also classified into this category.
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PAN, PQ. (2014). Criss-Cross Simplex Method. In: Linear Programming Computation. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40754-3_18
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