A Bidirectional Simplex Algorithm

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Abstract
A simplex type algorithm is presented which deals uniformly with (a) ordinary linear programming problems, (b) problems with upper bounded variables, and (c) problems with convex piecewise linear objective functions, e.g., absolute value terms. Problems of types (b) and (c) can be solved by suitable transformations into ordinary linear programming forms, but are handled by the unified algorithm without such transformations. Comparative computer runs indicate that direct solution by the unified algorithm is considerably more efficient than conversion into ordinary linear programming form followed by use of a regular simplex routine. Computer tests also show that the algorithm offers a worthwhile alternative to the use of artificial variables as a starting procedure for ordinary linear programming problems.

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