Characterizations of Approximate Optimality Conditions for Fractional Semi-Infinite Optimization Problems With Uncertainty
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摘要:
该文研究了一类带不确定参数的多目标分式半无限优化问题。首先借助鲁棒优化方法，引入该不确定多目标分式优化问题的鲁棒对应优化模型，并借助Dinkelbach方法，将该鲁棒对应优化模型转化为一般的多目标优化问题。随后借助一种标量化方法，建立了该优化问题的标量化问题，并刻画了它们的解之间的关系。最后借助一类鲁棒型次微分约束规格，建立了该不确定多目标分式优化问题拟近似有效解的鲁棒最优性条件。
Abstract:A class of multi-objective fractional semi-infinite optimization problems with uncertain data were investigated. Firstly, a robust optimization model corresponding to the uncertain multi-objective optimization problem was introduced. Then the optimization model was converted to a multi-objective optimization problem with the Dinkelbach method. In turn, by means of the scalarization method, the corresponding scalarization optimization problem was built, and the relationship between robust solutions to the multi-objective optimization problem and its corresponding scalarization optimization problem was described. Finally, through a robust-type sub-differential constraint qualification, the robust optimality condition for approximate quasi-efficient solutions to the multi-objective fractional optimization problem was established.
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