Existence of solutions of minimization problems with an increasing cost function and porosity
Zaslavski, Alexander J.
Abstr. Appl. Anal., Tome 2003 (2003) no. 7, p. 651-670 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
We consider the minimization problem $f(x) \rightarrow \mathrm{min}$ , $x\in K$ , where $K$ is a closed subset of an ordered Banach space $X$ and $f$ belongs to a space of increasing lower semicontinuous functions on $K$ . In our previous work, we showed that the complement of the set of all functions $f$ , 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 a $\sigma$ -porous set.
Publié le : 2003-06-16
Classification:  49J27,  90C30,  90C48 
@article{1056372944,
     author = {Zaslavski, Alexander J.},
     title = {Existence of solutions of minimization problems with an increasing cost function and porosity},
     journal = {Abstr. Appl. Anal.},
     volume = {2003},
     number = {7},
     year = {2003},
     pages = { 651-670},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1056372944}
}

Zaslavski, Alexander J. Existence of solutions of minimization problems with an increasing cost function and porosity. Abstr. Appl. Anal., Tome 2003 (2003) no. 7, pp.  651-670. http://gdmltest.u-ga.fr/item/1056372944/