Recent zbMATH articles in MSC 49K27https://www.zbmath.org/atom/cc/49K272021-07-26T21:45:41.944397ZWerkzeugOn a Bolza problemhttps://www.zbmath.org/1463.490332021-07-26T21:45:41.944397Z"Krastanov, Mikhail I."https://www.zbmath.org/authors/?q=ai:krastanov.mikhail-ivanov"Ribarska, Nadezhda K."https://www.zbmath.org/authors/?q=ai:ribarska.nadezhda-kIn this paper classical problem of the calculus of variations is investigated assuming that the integrand is a continuous function. The authors apply the main ideas of non-smooth analysis in order to prove a non-smooth version of the classical Euler equation. The usual assumption of existence of a common \( L^1 \)-upper bound of a family of summable functions is replaced by uniform integrability of the same family. The proposed in the paper technique do not use variational principles. A necessary optimality condition for the basic problem of calculus of variations is obtained.Closedness of the optimal solution sets for general vector alpha optimization problemshttps://www.zbmath.org/1463.901962021-07-26T21:45:41.944397Z"Su, Tran Van"https://www.zbmath.org/authors/?q=ai:su.tran-van"Hang, Dinh Dieu"https://www.zbmath.org/authors/?q=ai:hang.dinh-dieuSummary: The aim of paper is to study the closedness of the optimal solution sets for general vector alpha optimization problems in Hausdorff locally convex topological vector spaces. Firstly, we present the relationships between the optimal solution sets of primal and dual general vector alpha optimization problems. Secondly, making use of the upper semicontinuity of a set-valued mapping, we discuss the results on closedness of the optimal solution sets for general vector alpha optimization problems in infinite dimensional spaces.