Existence of solutions of minimization problems with an increasing cost function and porosity

[摘要] We consider the minimization problemf(x)→min,x∈K, whereKis a closed subset of an orderedBanach spaceXandfbelongs to a space of increasing lower semicontinuous functions onK. In our previous work, we showed that the complement of the set of all functionsf, for which the corresponding minimization problem has a solution, is of the first category. In the present paper we show that this complement is also aσ-porous set.

[学科分类] 数学（综合）