Geodesic
Application of the $\Lambda$–monotonicity to the search for optimal solutions in higher-dimensional problems
Contemporary Mathematics and Its Applications, Tome 95 (2015), pp. 65-71 
V. V. Kiselev. Application of the $\Lambda$–monotonicity to the search for optimal solutions in higher-dimensional problems. Contemporary Mathematics and Its Applications, Tome 95 (2015), pp. 65-71. http://geodesic.mathdoc.fr/item/CMA_2015_95_a5/
@article{CMA_2015_95_a5,
     author = {V. V. Kiselev},
     title = {Application of the $\Lambda${\textendash}monotonicity to the search for optimal solutions in higher-dimensional problems},
     journal = {Contemporary Mathematics and Its Applications},
     pages = {65--71},
     year = {2015},
     volume = {95},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMA_2015_95_a5/}
}
TY  - JOUR
AU  - V. V. Kiselev
TI  - Application of the $\Lambda$–monotonicity to the search for optimal solutions in higher-dimensional problems
JO  - Contemporary Mathematics and Its Applications
PY  - 2015
SP  - 65
EP  - 71
VL  - 95
UR  - http://geodesic.mathdoc.fr/item/CMA_2015_95_a5/
LA  - ru
ID  - CMA_2015_95_a5
ER  - 
%0 Journal Article
%A V. V. Kiselev
%T Application of the $\Lambda$–monotonicity to the search for optimal solutions in higher-dimensional problems
%J Contemporary Mathematics and Its Applications
%D 2015
%P 65-71
%V 95
%U http://geodesic.mathdoc.fr/item/CMA_2015_95_a5/
%G ru
%F CMA_2015_95_a5

Voir la notice de l'article provenant de la source Math-Net.Ru

The notion of Pareto optimality is widely used for solving many practical problems. The notion of $\Lambda$-optimality is a generalization of the Pareto optimality; the set of $\Lambda$-optimal solutions can be either wider or narrower than the set of Pareto-optimal solutions. In this paper, we generalize some results for $\Lambda$-optimal target functions obtained earlier, introduce the notion of a critical set of $\Lambda$-optimal solutions, and discuss certain approaches to construction of optimal solutions.