In the paper, we deal with the relations among several generalized second-order directional derivatives. The results partially solve the problem which of the second-order optimality conditions is more useful.
Článek představuje hru Kalaha a ukazuje, jak je možné ji při vyučování matematiky na 1. stupni, popřípadě v mateřské škole nebo v rodině, použít. První okruh her vychází přímo z pravidel této staré deskové hry a slouží k procvičování kombinatorického uvažování. Druhý okruh her pak slouží k nácviku numerace a procvičování základních numerických operací. Podobně jako šachová hra, má hra Kalaha bohatou historii, seznámením s touto hrou je tak možné přispět k mezipředmětovým vztahům matematiky a vlastivědy...
Vsevolod I. Ivanov stated (Nonlinear Analysis 125 (2015), 270-289) the general second-order optimality condition for the constrained vector problem in terms of Hadamard derivatives. We will consider its special case for a scalar problem and show some corollaries for example for -stable at feasible point functions. Then we show the advantages of obtained results with respect to the previously obtained results.
The aim of our article is to present a proof of the existence of local minimizer in the classical optimality problem without constraints under weaker assumptions in comparisons with common statements of the result. In addition we will provide rather elementary and self-contained proof of that result.
The notion of -stability is defined using the lower Dini directional derivatives and was introduced by the authors in their previous papers. In this paper we prove that the class of -stable functions coincides with the class of C functions. This also solves the question posed by the authors in SIAM J. Control Optim. 45 (1) (2006), pp. 383–387.
In the paper we present second-order necessary conditions for constrained vector optimization problems in infinite-dimensional spaces. In this way we generalize some corresponding results obtained earlier.
In the paper we generalize sufficient and necessary optimality conditions obtained by Ginchev, Guerraggio, Rocca, and by authors with the help of the notion of ℓ-stability for vector functions.
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