This paper deals with one of the canonical problems in networked systems - the resource allocation problem, that is based on user equilibrium principle. The user equilibrium principle was formulated in the middle of XX-th century by John Wardrop. Resource allocation problem has widespread applications. Urban road networks, financial networks, power grids and other systems could be modeled as network equilibrium problems with convex performance functions. The present paper is focused on the resource allocation problem with convex non-smooth piecewise linear nondecreasing performance function. The constructive tool to cope with such problem was developed.