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Linear superiorization (abbreviated: LinSup) considers linear programming(LP) problems wherein the constraints as well as the objective function arelinear. It allows to steer the iterates of a feasibility-seeking iterativeprocess toward feasible points that have lower (not necessarily minimal) valuesof the objective function than points that would have been reached by the samefeasiblity-seeking iterative process without superiorization. Using afeasibility-seeking iterative process that converges even if the linearfeasible set is empty, LinSup generates an iterative sequence that converges toa point that minimizes a proximity function which measures the linearconstraints violation. In addition, due to LinSup's repeated objective functionreduction steps such a point will most probably have a reduced objectivefunction value. We present an exploratory experimental result that illustratesthe behavior of LinSup on an infeasible LP problem.

Linear Superiorization for Infeasible Linear Programming