 
Summary: Comput. Maths. Math. Phys., Vol.33, No.12, pp. 15551568, 1993
Pergamon c
#1994 Elsevier Science Ltd
Printed in Great Britain. All rights reserved
09655425(94)E0014A
AN INTERIOR LINEARIZATION METHOD 1
A.S. ANTIPIN
Moscow
(Revised version 25 December 2002)
An interior linearization method is described. Its convergence to the solution of
the convex programming problem is proved. Bounds are obtained for the rate
of convergence. A relation with internal modied Lagrange functions methods
is established.
1. STATEMENT OF THE PROBLEM
Consider the convex programming problem
x # # Argmin {f(x) : g(x) # 0, x # Q}, (1.1)
where f(x) and each component of the vector function g(x) is a convex scalar function, and
Q # R n is a convex closed set in R n .
There are several approaches to the solution of this problem. One of these, based on the
gradient method, has been used as the basis of very many modications intended for the solution
