  A new exact projective penalty method is proposed for the equivalent
reduction of constrained optimization problems to nonsmooth unconstrained ones.
In the method, the original objective function is extended to infeasible points
by summing its value at the projection of an infeasible point on the feasible
set with the distance to the projection. Besides Euclidean projections, also a
pointed projection in the direction of some fixed internal feasible point can
be used. The equivalence means that local and global minimums of the problems
coincide. Nonconvex sets with multivalued Euclidean projections are admitted,
and the objective function may be lower semicontinuous. The particular case of
convex problems is included. The obtained unconstrained or box-constrained
problem is solved by a version of the branch and bound method combined with
local optimization. In principle, any local optimizer can be used within the
branch and bound scheme but in numerical experiments sequential quadratic
programming method was successfully used. So the proposed exact penalty method
does not assume the existence of the objective function outside the allowable
area and does not require the selection of the penalty coefficient.
