  Shor's r-algorithm (Shor, Zhurbenko (1971), Shor (1979)) with space
stretching in the direction of difference of two adjacent subgradients is a
competitive method of nonsmooth optimization. However, the original r-algorithm
is designed to minimize convex ravine functions without constraints. The
standard technique for solving constraint problems with this algorithm is to
use exact nonsmooth penalty functions (Eremin (1967), Zangwill (1967)). At the
same time, it is necessary to choose the (sufficiently large) penalty
coefficient in this method. In Norkin (2020, 2022) and Galvan et al. (2021),
the so-called projective exact penalty function method is proposed, which does
not formally require an exact definition of the penalty coefficient. In this
paper, a nonsmooth optimization problem with convex constraints is first
transformed into a constraintfree problem by the projective penalty function
method, and then the r-algorithm is applied to solve the transformed problem.
We present the results of testing this approach on problems with linear
constraints using a program implemented in Matlab.
