Measuring the Balance Space Sensitivity in Vector Optimization
Recent literature has shown that the balance space approach may be a significant alternative to address several topics concerning vector optimization. Although this new look also leads to the efficient set and, consequently, is equivalent to the classical viewpoint, it yields new results and algorithms, as well as new economic interpretations, that may be very useful in theoretical frameworks and practical applications. The present paper focuses on the sensitivity of the balance set. We prove a general envelope theorem that yields the sensitivity with respect to any parameter considered in the problem. Furthermore, we provide a dual problem that characterizes the primal balance space and its sensitivity. Finally, we also give the implications of our results with respect to the sensitivity of the efficient set.
KeywordsIdeal Point Vector Optimization Dual Solution Vector Optimization Problem Pareto Solution
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