Abstract
The study presents an approach to solve linear programming problems with no artificial variables. A primal linear minimization problem in standard form and its associated dual linear maximization problem are used. Initially, the dual (or a partial dual) program is solved by a "feasible direction" search, where the Karush-Kuhn-Tucker conditions help to verify its optimality and then its feasibility. The "feasible direction" search exploits the characteristics of the convex polyhedron (or polytope) formed by the dual program constraints to find a starting point and then follows line segments, whose directions are found in affine subspaces defined by boundary hyperplanes of polyhedral faces, to find next points up to the (an) optimal one. Then, the remaining dual constraints not satisfied at that optimal dual point, if there are any, are handled as nonbasic variables of the primal program, which is to be solved by such "feasible direction" search.
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