A computational tool assists in solving optimization problems that employ a variation of the simplex algorithm. This variation is particularly useful when an initial basic solution is infeasible, but optimality conditions are satisfied. The algorithm proceeds by maintaining optimality while iteratively driving the solution towards feasibility. For example, such a solver can efficiently address linear programs where adding constraints after an optimal solution is already known. The added constraints might render the existing solution infeasible, requiring a new solution approach.
Its significance lies in its ability to efficiently handle problems where the initial solution violates constraints. It provides a structured method for refining the solution, moving from an infeasible but optimal state to a feasible and optimal one. Historically, this algorithmic adaptation has allowed for faster resolution of certain types of linear programming problems. Its application proves beneficial in scenarios requiring dynamic modifications to existing optimization models, offering a powerful approach to re-optimization.
