On Efficient Solutions to Multiple Objective Mathematical Programs
探讨了拟有效解的性质及其与经典有效解的关系,证明了一个点是多目标数学规划的拟有效解当且仅当它是某个带非负权重的标量最大化问题的最优解,并据此将拟有效解集刻画为所有非空目标子集上有效解的并集。
This note develops properties of quasi-efficient solutions and explores interrelationships to the classical concept of efficiency. In particular, a point is a quasi-efficient solution to a multiple objective mathematical program if and only if it is an optimal solution to a scalar maximum problem for some set of nonnegative weights on the objectives. This result is then used to characterize the set of quasi-efficient solutions as the union of efficient solutions to a multiple objective problem over all nonempty subsets of the objectives.