What is the significance of dual feasibility in Linear Programming
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Dual feasibility ensures that the constraints of the dual problem are satisfied. It plays a key role in determining the optimality of the primal solution. A solution is optimal for the primal problem if it is both feasible and satisfies the complementary slackness conditions with the dual.
Dual feasibility in Linear Programming refers to the condition where the dual variables associated with the primal constraints are non-negative. This is significant because it ensures that the dual problem has a feasible solution, which is essential for the duality theorem. According to this theorem, if both the primal and dual problems are feasible, their optimal values are equal. Thus, ensuring dual feasibility helps in establishing optimality and understanding the relationship between the primal and dual formulations.
Dual feasibility in linear programming is important because it confirms that dual solutions satisfy the dual constraints, supporting the optimality of the primal solution. This relationship enhances understanding of duality principles, aids in sensitivity analysis, and is crucial for validating solutions and improving decision-making.