On Relations of Vector Optimization Results with C^(1,1) Data  

作　　者：Duan BEDNA■íK Karel PASTOR 

机构地区：[1]Department of Mathematics,University of Hradec Králové [2]Department of Mathematical Analysis and Applications of Mathematics,Faculty of Science,Palack■ University

出　　处：《Acta Mathematica Sinica,English Series》2010年第11期2031-2040,共10页数学学报（英文版）

基　　金：Supported by the Council of Czech Government (MSM 6198959214)

摘　　要：In this article we prove that some of the sufficient and necessary optimality conditions obtained by Ginchev, Guerraggio, Luc [Appl. Math., 51, 5-36 （2006）] generalize （strictly） those presented by Guerraggio, Luc [J. Optim. Theory Appl., 109, 615-629 （2001）]. While the former paper shows examples for which the conditions given there are effective but the ones from the latter paper fail, it does not prove that generally the conditions it proposes are stronger. In the present note we complete this comparison with the lacking proof.In this article we prove that some of the sufficient and necessary optimality conditions obtained by Ginchev, Guerraggio, Luc [Appl. Math., 51, 5-36 （2006）] generalize （strictly） those presented by Guerraggio, Luc [J. Optim. Theory Appl., 109, 615-629 （2001）]. While the former paper shows examples for which the conditions given there are effective but the ones from the latter paper fail, it does not prove that generally the conditions it proposes are stronger. In the present note we complete this comparison with the lacking proof.

关 键 词：C1＇1 function generalized second-order directional derivative Dini derivative weakly efficient minimizer isolated minimizer of second-order 

分 类 号：O224[理学—运筹学与控制论] TS102.311[理学—数学]