Summary: Dierential Equations, Vol. 30, No. 11, 1994, pp. 17031713
ON FINITE CONVERGENCE OF PROCESSES
TO A SHARP MINIMUM AND TO A SMOOTH MINIMUM
WITH A SHARP DERIVATIVE12
A.S. Antipin UDC 517.97+519.82
(Revised version 14 February 2003)
1. INTRODUCTION
Let us consider an illustrating example. The problem is to minimize the Euclidean norm in a
nite-dimensional space
x
Argmin{|x| : x Rn
}, (1.1)
where the function f(x) = |x| = (x2
1 + x2
2 + . . . + x2
n)1/2
is dierentiable everywhere except for the
origin and its gradient is f(x) = x/|x| (this can easily be checked by direct dierentiation of
the Euclidean norm). At the point x
= 0 the goal function has a sharp minimum. The gradient

Source: Antipin, Anatoly S. - Dorodnicyn Computing Centre of the Russian Academy of Sciences

Collections: Computer Technologies and Information Sciences; Mathematics