The unsolvability of vector discrete optimization problems in a class of algorithms of a linear convolution of criteria

In terms of systems of subsets, we describe a rather wide class of problems on combinatorial vector optimization which are unsolvable by the classical technique of linear convolution of criteria. This class includes, in particular, some well-known problems on graphs (the travelling salesman problem, the problem on a path between vertices and perfect matching problem, the problem on $p$-median and the problem on covering a graph by paths) as well as various Boolean programming problems with vector-valued criterion function being an arbitrary combination of criteria of the form $\maxsum$, $\maxmin$, $\maxmax$.
This work was partially supported by the Foundation for Basic Researches of the Republic of Byelorussia.