The upper semi-convergence of the set of approximation weakly efficient solutions for bi-level multi-objective stochastic programming
In order to study the convergence of approximation between the exact weakly efficient solution and the weakly efficient solution of the approximation problem of bi-level multi-objective stochastic programming,we construct an upper semi-convergence theoretical framework of weakly efficient solution sets for a class of approximation problems of multi-objective bi-level stochastic programming with both upper and lower constraints.In other words,on the premise of assuming that the optimal solution set function fed back from the lower layer to the upper layer is convex function,using the property of strict convex function,the weakly efficient solution of multi-objective stochastic programming can be expressed as the structural feature of the intersection of the opti-mal solution set of the corresponding single objective stochastic programming,and the upper semi-convergence of the approximation of the weakly efficient solution set by the bi-level multi-objec-tive stochastic programming is established.This conclusion provides the theorectical basis that approximation weakly effective solution sets can approximately replace the exact weakly effective solution sets in bi-level multi-objective stochastic programming.
single objective stochastic programmingmulti-objective stochastic programmingweakly efficient solution setsstrictly convex function
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