Stability of a combinatorial vector partition problem

Abstract

The vector variant of the partition problem is considered. It is shown that the coincidence of the Pareto and Slater sets is the necessary and sufficient condition of stability of the problem with respect to its functional.

Combinatorial optimization under uncertainty

“…The fourth approach to the description of uncertainty can be analyzed by means of stability and parametrical analysis [4]. The fifth type of uncertainty can be analyzed by methods of vector optimization [5,[40][41][42][43][44][45].…”

Boolean problem of sequential minimization of moduli of linear functions and stability theorems

“…In particular, based on the use of properties of point-set mappings, a comparative analysis of five types of stability with respect to functionals and constraints of vector integer problems with linear and quadratic partial criterions is made in [6][7][8] (see also [9,10] in which these and many other results are systematized). The mentioned works, as well as other achievements of the collective, substantially stimulated investigations of similar problems in Russia (for example, [11][12][13][14]*), Belarus (for example, [15][16][17][18][19][20][21][22][23][24][25][26][27]*), Poland [28,29], and other countries [30].…”