Abstract :
We consider a problem of minimization of convex function f x. over the convex
region R where the objective function and the feasible region have a common
direction of recession. In cases when one of these directions is not in the constancy
space of the objective function, then the minimal solution is not achieved even if
the function f x. is bounded below over the region R. Many algorithms, if applied
to this class of programmes, do not guarantee convergence to the global infimum.
Our approach to this problem leads to derivation of the equation of the feasible
parametrized curve C t., such that the infimum of the logarithmic penalty function
along this curve is equal to the global infimum of the objective function over the
region R. We show that if all functions defining the program are analytic, then
C t. is also an analytic function. The equation of the curve can be successfully used
to determine the global infimum in particular, unboundedness.of the convex
constrained programmes in cases when the application of classical methods, such
as the steepest descent method, fails to converge to the global infimum
