In this paper, we obtain the Painleve-Kuratowski Convergence of the efficient solution sets, the weak efficient solution sets and various proper efficient solution sets for the perturbed generalized system with a sequ...In this paper, we obtain the Painleve-Kuratowski Convergence of the efficient solution sets, the weak efficient solution sets and various proper efficient solution sets for the perturbed generalized system with a sequence of mappings converging in a real locally convex Hausdorff topological vector spaces.展开更多
In this paper, stability results of solution mappings to perturbed vector generalized system are studied. Firstly, without the assumption of monotonicity, the Painleve-Kuratowski convergence of global efficient soluti...In this paper, stability results of solution mappings to perturbed vector generalized system are studied. Firstly, without the assumption of monotonicity, the Painleve-Kuratowski convergence of global efficient solution sets of a family of perturbed problems to the corresponding global efficient solution set of the generalized system is obtained, where the perturbations are performed on both the objective function and the feasible set. Then, the density and Painleve-Kuratowski convergence results of efficient solution sets are established by using gamma convergence, which is weaker than the assumption of continuous convergence. These results extend and improve the recent ones in the literature.展开更多
We prove the following main result: Let X be a normed linear space,fn ∈ X*\{θ},Hn = {x ∈ X: fn(x) = l},n = 0, 1,2,...Then w* - limfn = f0 iff H0 lim inf Hn and θ limsup Hn; when X is a reflexive Banach space, l...We prove the following main result: Let X be a normed linear space,fn ∈ X*\{θ},Hn = {x ∈ X: fn(x) = l},n = 0, 1,2,...Then w* - limfn = f0 iff H0 lim inf Hn and θ limsup Hn; when X is a reflexive Banach space, lim ||fn - f0|| = 0. If and only if θ w-limsup Hn Ho It simplifies the related results in [1].展开更多
基金Supported by the National Natural Science Foundation of China (No. 10871216 and 11171362)
文摘In this paper, we obtain the Painleve-Kuratowski Convergence of the efficient solution sets, the weak efficient solution sets and various proper efficient solution sets for the perturbed generalized system with a sequence of mappings converging in a real locally convex Hausdorff topological vector spaces.
基金Supported by the National Natural Science Foundation of China(No.11431004.11471059.11401058)the Basic and Advanced Research Project of Chongqing(cstc2017jcyj AX0382,cstc2015shmszx30004)+1 种基金the Program for University Innovation Team of Chongqing(CXTDX201601022)the Education Committee Project Foundation of Bayu Scholar
文摘In this paper, stability results of solution mappings to perturbed vector generalized system are studied. Firstly, without the assumption of monotonicity, the Painleve-Kuratowski convergence of global efficient solution sets of a family of perturbed problems to the corresponding global efficient solution set of the generalized system is obtained, where the perturbations are performed on both the objective function and the feasible set. Then, the density and Painleve-Kuratowski convergence results of efficient solution sets are established by using gamma convergence, which is weaker than the assumption of continuous convergence. These results extend and improve the recent ones in the literature.
文摘We prove the following main result: Let X be a normed linear space,fn ∈ X*\{θ},Hn = {x ∈ X: fn(x) = l},n = 0, 1,2,...Then w* - limfn = f0 iff H0 lim inf Hn and θ limsup Hn; when X is a reflexive Banach space, lim ||fn - f0|| = 0. If and only if θ w-limsup Hn Ho It simplifies the related results in [1].
